Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/4609
Title: What is a first countable space?
Authors: Gutierres, Gonçalo 
Keywords: First countable space; Axiom of Choice
Issue Date: 2006
Citation: Topology and its Applications. 153:18 (2006) 3420-3429
Abstract: The definition of first countable space is standard and its meaning is very clear. But is that the case in the absence of the Axiom of Choice? The answer is negative because there are at least three choice-free versions of first countability. And, most likely, the usual definition does not correspond to what we want to be a first countable space. The three definitions as well as other characterizations of first countability are presented and it is discussed under which set-theoretic conditions they remain equivalent.
URI: http://hdl.handle.net/10316/4609
DOI: 10.1016/j.topol.2006.03.003
Rights: openAccess
Appears in Collections:FCTUC Matemática - Artigos em Revistas Internacionais

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