Sandwich-type characterization of completely regular spaces | Zendy

Javier Gutiérrez García | Zendy

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Sandwich-type characterization of completely regular spaces

Author(s) -

Javier Gutiérrez García

Publication year - 2007

Publication title -

applied general topology

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.638

H-Index - 13

eISSN - 1989-4147

pISSN - 1576-9402

DOI - 10.4995/agt.2007.1887

Subject(s) - tychonoff space , mathematics , separation axiom , characterization (materials science) , regular space , type (biology) , corollary , axiom , extension (predicate logic) , pure mathematics , function space , topological space , space (punctuation) , continuous function (set theory) , function (biology) , topology (electrical circuits) , discrete mathematics , combinatorics , geometry , computer science , ecology , materials science , evolutionary biology , biology , programming language , nanotechnology , operating system

All the higher separation axioms in topology, except for complete regularity, are known to have sandwich-type characterizations. This note provides a characterization of complete regularity in terms of inserting a continuous real-valued function. The known fact that each continuous real valued function on a compact subset o fa Tychonoff space has a continuous extension to the whole space is obtained as a corollary

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