Properties of the Ceder Product
We study properties of the Ceder product X × b Y of topological spaces X and Y, where b ∈ Y, recently introduced by the authors. Important examples of the Ceder product are the Ceder plane and the Alexandroff double circle. In particular, for i = 0 , 1 , 2 , 3 we establish necessary and sufficient c...
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| Veröffentlicht in: | Ukrainian mathematical journal 2015-11, Vol.67 (6), p.881-890 |
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| container_title | Ukrainian mathematical journal |
| container_volume | 67 |
| creator | Maslyuchenko, V. K. Maslyuchenko, O. V. Myronyk, O. D. |
| description | We study properties of the Ceder product
X ×
b
Y
of topological spaces
X
and
Y,
where
b ∈ Y,
recently introduced by the authors. Important examples of the Ceder product are the Ceder plane and the Alexandroff double circle. In particular, for
i
= 0
,
1
,
2
,
3 we establish necessary and sufficient conditions for the Ceder product to be a
T
i
-space. We prove that the Ceder product
X ×
b
Y
is metrizable if and only if the spaces
X
and
Y
.
=
Y
\
b
are metrizable,
X
is σ-discrete, and the set
{b}
is closed in
Y.
If
X
is not discrete, then the point
b
has a countable base of closed neighborhoods in
Y. |
| doi_str_mv | 10.1007/s11253-015-1120-2 |
| format | Article |
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X ×
b
Y
of topological spaces
X
and
Y,
where
b ∈ Y,
recently introduced by the authors. Important examples of the Ceder product are the Ceder plane and the Alexandroff double circle. In particular, for
i
= 0
,
1
,
2
,
3 we establish necessary and sufficient conditions for the Ceder product to be a
T
i
-space. We prove that the Ceder product
X ×
b
Y
is metrizable if and only if the spaces
X
and
Y
.
=
Y
\
b
are metrizable,
X
is σ-discrete, and the set
{b}
is closed in
Y.
If
X
is not discrete, then the point
b
has a countable base of closed neighborhoods in
Y.</description><identifier>ISSN: 0041-5995</identifier><identifier>EISSN: 1573-9376</identifier><identifier>DOI: 10.1007/s11253-015-1120-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Mathematics ; Mathematics and Statistics ; Statistics</subject><ispartof>Ukrainian mathematical journal, 2015-11, Vol.67 (6), p.881-890</ispartof><rights>Springer Science+Business Media New York 2015</rights><rights>COPYRIGHT 2015 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c279t-f63c927818c593f9888d2e8d59bfb88723e9a60b45f1185676c7c56a42e282f33</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11253-015-1120-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11253-015-1120-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Maslyuchenko, V. K.</creatorcontrib><creatorcontrib>Maslyuchenko, O. V.</creatorcontrib><creatorcontrib>Myronyk, O. D.</creatorcontrib><title>Properties of the Ceder Product</title><title>Ukrainian mathematical journal</title><addtitle>Ukr Math J</addtitle><description>We study properties of the Ceder product
X ×
b
Y
of topological spaces
X
and
Y,
where
b ∈ Y,
recently introduced by the authors. Important examples of the Ceder product are the Ceder plane and the Alexandroff double circle. In particular, for
i
= 0
,
1
,
2
,
3 we establish necessary and sufficient conditions for the Ceder product to be a
T
i
-space. We prove that the Ceder product
X ×
b
Y
is metrizable if and only if the spaces
X
and
Y
.
=
Y
\
b
are metrizable,
X
is σ-discrete, and the set
{b}
is closed in
Y.
If
X
is not discrete, then the point
b
has a countable base of closed neighborhoods in
Y.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Statistics</subject><issn>0041-5995</issn><issn>1573-9376</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMouFZ_gCf3D6ROks3XsRS_oKAHPYdsdlK3tLsl2R7896asZ5nDDC_zDMxDyD2DJQPQj5kxLgUFJmmZgPILUjGpBbVCq0tSATSMSmvlNbnJeQdQKKMr8vCRxiOmqcdcj7GevrFeY4epLnl3CtMtuYp-n_Hury_I1_PT5_qVbt5f3tarDQ1c24lGJYLl2jATpBXRGmM6jqaTto2tMZoLtF5B28jImJFKq6CDVL7hyA2PQizIcr679Xt0_RDHKflQqsNDH8YBY1_yVdMIa0ECFIDNQEhjzgmjO6b-4NOPY-DOStysxBUl7qzE8cLwmclld9hicrvxlIby1z_QL4MvYOI</recordid><startdate>20151101</startdate><enddate>20151101</enddate><creator>Maslyuchenko, V. K.</creator><creator>Maslyuchenko, O. V.</creator><creator>Myronyk, O. D.</creator><general>Springer US</general><general>Springer</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20151101</creationdate><title>Properties of the Ceder Product</title><author>Maslyuchenko, V. K. ; Maslyuchenko, O. V. ; Myronyk, O. D.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c279t-f63c927818c593f9888d2e8d59bfb88723e9a60b45f1185676c7c56a42e282f33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Statistics</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Maslyuchenko, V. K.</creatorcontrib><creatorcontrib>Maslyuchenko, O. V.</creatorcontrib><creatorcontrib>Myronyk, O. D.</creatorcontrib><collection>CrossRef</collection><jtitle>Ukrainian mathematical journal</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Maslyuchenko, V. K.</au><au>Maslyuchenko, O. V.</au><au>Myronyk, O. D.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Properties of the Ceder Product</atitle><jtitle>Ukrainian mathematical journal</jtitle><stitle>Ukr Math J</stitle><date>2015-11-01</date><risdate>2015</risdate><volume>67</volume><issue>6</issue><spage>881</spage><epage>890</epage><pages>881-890</pages><issn>0041-5995</issn><eissn>1573-9376</eissn><abstract>We study properties of the Ceder product
X ×
b
Y
of topological spaces
X
and
Y,
where
b ∈ Y,
recently introduced by the authors. Important examples of the Ceder product are the Ceder plane and the Alexandroff double circle. In particular, for
i
= 0
,
1
,
2
,
3 we establish necessary and sufficient conditions for the Ceder product to be a
T
i
-space. We prove that the Ceder product
X ×
b
Y
is metrizable if and only if the spaces
X
and
Y
.
=
Y
\
b
are metrizable,
X
is σ-discrete, and the set
{b}
is closed in
Y.
If
X
is not discrete, then the point
b
has a countable base of closed neighborhoods in
Y.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s11253-015-1120-2</doi><tpages>10</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0041-5995 |
| ispartof | Ukrainian mathematical journal, 2015-11, Vol.67 (6), p.881-890 |
| issn | 0041-5995 1573-9376 |
| language | eng |
| recordid | cdi_gale_infotracacademiconefile_A443990500 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Statistics |
| title | Properties of the Ceder Product |
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