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...

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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
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Zusammenfassung: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.)
ISSN:0002-9890
1930-0972