On Distality of a Transformation Semigroup with One Point Compactification of a Discrete Space as Phase Space
For infinite discrete topological space Y , suppose A ( Y ) is one point compactification of Y , in the following text we prove that the transformation semigroup ( A ( Y ) , S ) is distal if and only if the enveloping semigroup E ( A ( Y ) , S ) is a group of homeomorphisms on A ( Y ) , or equivalen...
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| Veröffentlicht in: | Iranian journal of science and technology. Transaction A, Science Science, 2016-12, Vol.40 (4), p.209-217 |
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| container_title | Iranian journal of science and technology. Transaction A, Science |
| container_volume | 40 |
| creator | Ayatollah Zadeh Shirazi, Fatemah Mahmoodi, Mohammad Ali Raeisi, Morvarid |
| description | For infinite discrete topological space
Y
,
suppose
A
(
Y
)
is one point compactification of
Y
,
in the following text we prove that the transformation semigroup
(
A
(
Y
)
,
S
)
is distal if and only if the enveloping semigroup
E
(
A
(
Y
)
,
S
)
is a group of homeomorphisms on
A
(
Y
)
,
or equivalently for all
p
∈
E
(
A
(
Y
)
,
S
)
,
p
:
A
(
Y
)
→
A
(
Y
)
is pointwise periodic. Also, the transformation group
(
A
(
Y
)
,
S
)
is distal (resp. equicontinuous, pointwise minimal) if and only if for all
x
∈
A
(
Y
)
,
x
S
is a finite subset of
A
(
Y
)
. The text is motivated with tables, counterexamples and studying finally distality (and co-decomposability to distal transformation semigroups) in the abelian transformation semigroup
(
A
(
Y
)
,
S
)
. |
| doi_str_mv | 10.1007/s40995-016-0095-7 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2133380477</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2133380477</sourcerecordid><originalsourceid>FETCH-LOGICAL-c268t-7098563ff8724debe000cf91a1964dd53d720724703fd9e8b71b264daa5f3d8f3</originalsourceid><addsrcrecordid>eNp1kF9rwyAUxWVssNL1A-xN2HO2qyaaPI7uLxRaaPcsJtHW0cRMLaPffnYp7GlP18s5v3PlIHRL4J4AiIeQQ1UVGRCeAaSHuEATyniekZJUl2hCgJYZp4Jfo1kItgZGCBc05xPULXv8ZENUexuP2Bms8MarPhjnOxWt6_Fad3br3WHA3zbu8LLXeOVsH_HcdYNqojW2GZ2_dAprvI4ar5OosQp4tVPhvN6gK6P2Qc_Oc4o-Xp4387dssXx9nz8usobyMmYCqrLgzJgyfbLVtQaAxlREkYrnbVuwVlBIkgBm2kqXtSA1TYpShWFtadgU3Y25g3dfBx2i_HQH36eTkhLGWAm5EMlFRlfjXQheGzl42yl_lATkqVg5FitTsfJUrDwxdGRC8vZb7f-S_4d-ANeUeus</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2133380477</pqid></control><display><type>article</type><title>On Distality of a Transformation Semigroup with One Point Compactification of a Discrete Space as Phase Space</title><source>Alma/SFX Local Collection</source><creator>Ayatollah Zadeh Shirazi, Fatemah ; Mahmoodi, Mohammad Ali ; Raeisi, Morvarid</creator><creatorcontrib>Ayatollah Zadeh Shirazi, Fatemah ; Mahmoodi, Mohammad Ali ; Raeisi, Morvarid</creatorcontrib><description>For infinite discrete topological space
Y
,
suppose
A
(
Y
)
is one point compactification of
Y
,
in the following text we prove that the transformation semigroup
(
A
(
Y
)
,
S
)
is distal if and only if the enveloping semigroup
E
(
A
(
Y
)
,
S
)
is a group of homeomorphisms on
A
(
Y
)
,
or equivalently for all
p
∈
E
(
A
(
Y
)
,
S
)
,
p
:
A
(
Y
)
→
A
(
Y
)
is pointwise periodic. Also, the transformation group
(
A
(
Y
)
,
S
)
is distal (resp. equicontinuous, pointwise minimal) if and only if for all
x
∈
A
(
Y
)
,
x
S
is a finite subset of
A
(
Y
)
. The text is motivated with tables, counterexamples and studying finally distality (and co-decomposability to distal transformation semigroups) in the abelian transformation semigroup
(
A
(
Y
)
,
S
)
.</description><identifier>ISSN: 1028-6276</identifier><identifier>EISSN: 2364-1819</identifier><identifier>DOI: 10.1007/s40995-016-0095-7</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Chemistry/Food Science ; Earth Sciences ; Engineering ; Life Sciences ; Materials Science ; Physics ; Research Paper ; Topology</subject><ispartof>Iranian journal of science and technology. Transaction A, Science, 2016-12, Vol.40 (4), p.209-217</ispartof><rights>Shiraz University 2016</rights><rights>Copyright Springer Science & Business Media 2016</rights><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c268t-7098563ff8724debe000cf91a1964dd53d720724703fd9e8b71b264daa5f3d8f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,776,780,27901,27902</link.rule.ids></links><search><creatorcontrib>Ayatollah Zadeh Shirazi, Fatemah</creatorcontrib><creatorcontrib>Mahmoodi, Mohammad Ali</creatorcontrib><creatorcontrib>Raeisi, Morvarid</creatorcontrib><title>On Distality of a Transformation Semigroup with One Point Compactification of a Discrete Space as Phase Space</title><title>Iranian journal of science and technology. Transaction A, Science</title><addtitle>Iran J Sci Technol Trans Sci</addtitle><description>For infinite discrete topological space
Y
,
suppose
A
(
Y
)
is one point compactification of
Y
,
in the following text we prove that the transformation semigroup
(
A
(
Y
)
,
S
)
is distal if and only if the enveloping semigroup
E
(
A
(
Y
)
,
S
)
is a group of homeomorphisms on
A
(
Y
)
,
or equivalently for all
p
∈
E
(
A
(
Y
)
,
S
)
,
p
:
A
(
Y
)
→
A
(
Y
)
is pointwise periodic. Also, the transformation group
(
A
(
Y
)
,
S
)
is distal (resp. equicontinuous, pointwise minimal) if and only if for all
x
∈
A
(
Y
)
,
x
S
is a finite subset of
A
(
Y
)
. The text is motivated with tables, counterexamples and studying finally distality (and co-decomposability to distal transformation semigroups) in the abelian transformation semigroup
(
A
(
Y
)
,
S
)
.</description><subject>Chemistry/Food Science</subject><subject>Earth Sciences</subject><subject>Engineering</subject><subject>Life Sciences</subject><subject>Materials Science</subject><subject>Physics</subject><subject>Research Paper</subject><subject>Topology</subject><issn>1028-6276</issn><issn>2364-1819</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>8G5</sourceid><sourceid>BENPR</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNp1kF9rwyAUxWVssNL1A-xN2HO2qyaaPI7uLxRaaPcsJtHW0cRMLaPffnYp7GlP18s5v3PlIHRL4J4AiIeQQ1UVGRCeAaSHuEATyniekZJUl2hCgJYZp4Jfo1kItgZGCBc05xPULXv8ZENUexuP2Bms8MarPhjnOxWt6_Fad3br3WHA3zbu8LLXeOVsH_HcdYNqojW2GZ2_dAprvI4ar5OosQp4tVPhvN6gK6P2Qc_Oc4o-Xp4387dssXx9nz8usobyMmYCqrLgzJgyfbLVtQaAxlREkYrnbVuwVlBIkgBm2kqXtSA1TYpShWFtadgU3Y25g3dfBx2i_HQH36eTkhLGWAm5EMlFRlfjXQheGzl42yl_lATkqVg5FitTsfJUrDwxdGRC8vZb7f-S_4d-ANeUeus</recordid><startdate>20161201</startdate><enddate>20161201</enddate><creator>Ayatollah Zadeh Shirazi, Fatemah</creator><creator>Mahmoodi, Mohammad Ali</creator><creator>Raeisi, Morvarid</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>7U5</scope><scope>7WY</scope><scope>7XB</scope><scope>883</scope><scope>8AF</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AEUYN</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>ATCPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>BHPHI</scope><scope>CCPQU</scope><scope>CWDGH</scope><scope>D1I</scope><scope>DWQXO</scope><scope>FR3</scope><scope>FRNLG</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>H8D</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>KB.</scope><scope>KR7</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0F</scope><scope>M2O</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PATMY</scope><scope>PDBOC</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>PYCSY</scope><scope>Q9U</scope></search><sort><creationdate>20161201</creationdate><title>On Distality of a Transformation Semigroup with One Point Compactification of a Discrete Space as Phase Space</title><author>Ayatollah Zadeh Shirazi, Fatemah ; Mahmoodi, Mohammad Ali ; Raeisi, Morvarid</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c268t-7098563ff8724debe000cf91a1964dd53d720724703fd9e8b71b264daa5f3d8f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Chemistry/Food Science</topic><topic>Earth Sciences</topic><topic>Engineering</topic><topic>Life Sciences</topic><topic>Materials Science</topic><topic>Physics</topic><topic>Research Paper</topic><topic>Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Ayatollah Zadeh Shirazi, Fatemah</creatorcontrib><creatorcontrib>Mahmoodi, Mohammad Ali</creatorcontrib><creatorcontrib>Raeisi, Morvarid</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>ABI/INFORM Collection</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Trade & Industry (Alumni Edition)</collection><collection>STEM Database</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest One Sustainability</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>Agricultural & Environmental Science Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Business Premium Collection</collection><collection>Technology Collection (ProQuest)</collection><collection>Natural Science Collection</collection><collection>ProQuest One Community College</collection><collection>Middle East & Africa Database</collection><collection>ProQuest Materials Science Collection</collection><collection>ProQuest Central Korea</collection><collection>Engineering Research Database</collection><collection>Business Premium Collection (Alumni)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer Science Database</collection><collection>Materials Science Database</collection><collection>Civil Engineering Abstracts</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Trade & Industry</collection><collection>Research Library</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Environmental Science Database</collection><collection>Materials Science Collection</collection><collection>ProQuest One Business</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering Collection</collection><collection>Environmental Science Collection</collection><collection>ProQuest Central Basic</collection><jtitle>Iranian journal of science and technology. Transaction A, Science</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ayatollah Zadeh Shirazi, Fatemah</au><au>Mahmoodi, Mohammad Ali</au><au>Raeisi, Morvarid</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Distality of a Transformation Semigroup with One Point Compactification of a Discrete Space as Phase Space</atitle><jtitle>Iranian journal of science and technology. Transaction A, Science</jtitle><stitle>Iran J Sci Technol Trans Sci</stitle><date>2016-12-01</date><risdate>2016</risdate><volume>40</volume><issue>4</issue><spage>209</spage><epage>217</epage><pages>209-217</pages><issn>1028-6276</issn><eissn>2364-1819</eissn><abstract>For infinite discrete topological space
Y
,
suppose
A
(
Y
)
is one point compactification of
Y
,
in the following text we prove that the transformation semigroup
(
A
(
Y
)
,
S
)
is distal if and only if the enveloping semigroup
E
(
A
(
Y
)
,
S
)
is a group of homeomorphisms on
A
(
Y
)
,
or equivalently for all
p
∈
E
(
A
(
Y
)
,
S
)
,
p
:
A
(
Y
)
→
A
(
Y
)
is pointwise periodic. Also, the transformation group
(
A
(
Y
)
,
S
)
is distal (resp. equicontinuous, pointwise minimal) if and only if for all
x
∈
A
(
Y
)
,
x
S
is a finite subset of
A
(
Y
)
. The text is motivated with tables, counterexamples and studying finally distality (and co-decomposability to distal transformation semigroups) in the abelian transformation semigroup
(
A
(
Y
)
,
S
)
.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s40995-016-0095-7</doi><tpages>9</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1028-6276 |
| ispartof | Iranian journal of science and technology. Transaction A, Science, 2016-12, Vol.40 (4), p.209-217 |
| issn | 1028-6276 2364-1819 |
| language | eng |
| recordid | cdi_proquest_journals_2133380477 |
| source | Alma/SFX Local Collection |
| subjects | Chemistry/Food Science Earth Sciences Engineering Life Sciences Materials Science Physics Research Paper Topology |
| title | On Distality of a Transformation Semigroup with One Point Compactification of a Discrete Space as Phase Space |
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