A better framework for first countable spaces | Zendy

Gerhard Preuß | Zendy

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A better framework for first countable spaces

Author(s) -

Gerhard Preuß

Publication year - 2003

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.2003.2034

Subject(s) - mathematics , countable set , cosmic space , topological space , quotient , isolated point , space (punctuation) , function space , context (archaeology) , pure mathematics , connected space , topological vector space , topology (electrical circuits) , discrete mathematics , combinatorics , computer science , paleontology , biology , operating system

In the realm of semiuniform convergence spaces first countability is divisible and leads to a well-behaved topological construct with natural function spaces and one-point extensions such that countable products of quotients are quotients. Every semiuniform convergence space (e.g. symmetric topological space, uniform space, filter space, etc.) has an underlying first countable space. Several applications of first countability in a broader context than the usual one of topological spaces are studied

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