Autor(es):
Gutierres, Gonçalo 
Data: 2006
Identificador Persistente: http://hdl.handle.net/10316/4609
Origem: Estudo Geral - Universidade de Coimbra
Assunto(s): First countable space; Axiom of Choice
Detalhes do Documento
What is a first countable space?
Descrição
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. http://www.sciencedirect.com/science/article/B6V1K-4JW7WM9-1/1/4025b9614c54388284b3ddebaaa8e75b
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. http://www.sciencedirect.com/science/article/B6V1K-4JW7WM9-1/1/4025b9614c54388284b3ddebaaa8e75b
Tipo de Documento
Artigo
Idioma Inglês
Idioma Inglês
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