A Characterization of Continuity Revisited

A Characterization of Continuity Revisited

It is well known that a function f : R ... R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2...-dimensional linear spaces of nowhere continuous functions that (except for the zero functio...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:The American mathematical monthly 2011-02, Vol.118 (2), p.1
Hauptverfasser: Gámez-Merino, José L, Muñoz-Fernández, Gustavo A, Seoane-Sepúlveda, Juan B
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical functions
Mathematical problems
Set theory
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue 2
container_start_page 1
container_title The American mathematical monthly
container_volume 118
creator Gámez-Merino, José L
Muñoz-Fernández, Gustavo A
Seoane-Sepúlveda, Juan B
description It is well known that a function f : R ... R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2...-dimensional linear spaces of nowhere continuous functions that (except for the zero function) transform compact sets into compact sets and connected sets into connected sets respectively. (ProQuest: ... denotes formulae/symbols omitted.)
format Article
fullrecord <record><control><sourceid>proquest</sourceid><recordid>TN_cdi_proquest_journals_863557462</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2330558151</sourcerecordid><originalsourceid>FETCH-proquest_journals_8635574623</originalsourceid><addsrcrecordid>eNpjYuA0tDQ20DWwNDdiYeA0MDAw0rW0sDTgYOAqLs4Ccg1MTYw4GbQcFZwzEosSk0tSizKrEksy8_MU8tMUnPPzSjLzSjNLKhWCUssyizNLUlN4GFjTEnOKU3mhNDeDkptriLOHbkFRfmFpanFJfFZ-aVEeUCrewszY1NTcxMzImChFAI94MeU</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>863557462</pqid></control><display><type>article</type><title>A Characterization of Continuity Revisited</title><source>JSTOR Mathematics &amp; Statistics</source><source>JSTOR Archive Collection A-Z Listing</source><source>EZB-FREE-00999 freely available EZB journals</source><source>Alma/SFX Local Collection</source><creator>Gámez-Merino, José L ; Muñoz-Fernández, Gustavo A ; Seoane-Sepúlveda, Juan B</creator><creatorcontrib>Gámez-Merino, José L ; Muñoz-Fernández, Gustavo A ; Seoane-Sepúlveda, Juan B</creatorcontrib><description>It is well known that a function f : R ... R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2...-dimensional linear spaces of nowhere continuous functions that (except for the zero function) transform compact sets into compact sets and connected sets into connected sets respectively. (ProQuest: ... denotes formulae/symbols omitted.)</description><identifier>ISSN: 0002-9890</identifier><identifier>EISSN: 1930-0972</identifier><identifier>CODEN: AMMYAE</identifier><language>eng</language><publisher>Washington: Taylor &amp; Francis Ltd</publisher><subject>Mathematical functions ; Mathematical problems ; Set theory</subject><ispartof>The American mathematical monthly, 2011-02, Vol.118 (2), p.1</ispartof><rights>Copyright Mathematical Association Of America Feb 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784</link.rule.ids></links><search><creatorcontrib>Gámez-Merino, José L</creatorcontrib><creatorcontrib>Muñoz-Fernández, Gustavo A</creatorcontrib><creatorcontrib>Seoane-Sepúlveda, Juan B</creatorcontrib><title>A Characterization of Continuity Revisited</title><title>The American mathematical monthly</title><description>It is well known that a function f : R ... R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2...-dimensional linear spaces of nowhere continuous functions that (except for the zero function) transform compact sets into compact sets and connected sets into connected sets respectively. (ProQuest: ... denotes formulae/symbols omitted.)</description><subject>Mathematical functions</subject><subject>Mathematical problems</subject><subject>Set theory</subject><issn>0002-9890</issn><issn>1930-0972</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNpjYuA0tDQ20DWwNDdiYeA0MDAw0rW0sDTgYOAqLs4Ccg1MTYw4GbQcFZwzEosSk0tSizKrEksy8_MU8tMUnPPzSjLzSjNLKhWCUssyizNLUlN4GFjTEnOKU3mhNDeDkptriLOHbkFRfmFpanFJfFZ-aVEeUCrewszY1NTcxMzImChFAI94MeU</recordid><startdate>20110201</startdate><enddate>20110201</enddate><creator>Gámez-Merino, José L</creator><creator>Muñoz-Fernández, Gustavo A</creator><creator>Seoane-Sepúlveda, Juan B</creator><general>Taylor &amp; Francis Ltd</general><scope>JQ2</scope></search><sort><creationdate>20110201</creationdate><title>A Characterization of Continuity Revisited</title><author>Gámez-Merino, José L ; Muñoz-Fernández, Gustavo A ; Seoane-Sepúlveda, Juan B</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-proquest_journals_8635574623</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Mathematical functions</topic><topic>Mathematical problems</topic><topic>Set theory</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Gámez-Merino, José L</creatorcontrib><creatorcontrib>Muñoz-Fernández, Gustavo A</creatorcontrib><creatorcontrib>Seoane-Sepúlveda, Juan B</creatorcontrib><collection>ProQuest Computer Science Collection</collection><jtitle>The American mathematical monthly</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Gámez-Merino, José L</au><au>Muñoz-Fernández, Gustavo A</au><au>Seoane-Sepúlveda, Juan B</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A Characterization of Continuity Revisited</atitle><jtitle>The American mathematical monthly</jtitle><date>2011-02-01</date><risdate>2011</risdate><volume>118</volume><issue>2</issue><spage>1</spage><pages>1-</pages><issn>0002-9890</issn><eissn>1930-0972</eissn><coden>AMMYAE</coden><abstract>It is well known that a function f : R ... R is continuous if and only if the image of every compact set under f is compact and the image of every connected set is connected. We show that there exist two 2...-dimensional linear spaces of nowhere continuous functions that (except for the zero function) transform compact sets into compact sets and connected sets into connected sets respectively. (ProQuest: ... denotes formulae/symbols omitted.)</abstract><cop>Washington</cop><pub>Taylor &amp; Francis Ltd</pub></addata></record>
fulltext fulltext
identifier ISSN: 0002-9890
ispartof The American mathematical monthly, 2011-02, Vol.118 (2), p.1
issn 0002-9890
1930-0972
language eng
recordid cdi_proquest_journals_863557462
source JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection
subjects Mathematical functions
Mathematical problems
Set theory
title A Characterization of Continuity Revisited
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T11%3A35%3A40IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=A%20Characterization%20of%20Continuity%20Revisited&rft.jtitle=The%20American%20mathematical%20monthly&rft.au=G%C3%A1mez-Merino,%20Jos%C3%A9%20L&rft.date=2011-02-01&rft.volume=118&rft.issue=2&rft.spage=1&rft.pages=1-&rft.issn=0002-9890&rft.eissn=1930-0972&rft.coden=AMMYAE&rft_id=info:doi/&rft_dat=%3Cproquest%3E2330558151%3C/proquest%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=863557462&rft_id=info:pmid/&rfr_iscdi=true