Author(s):
Gutierres, Gonçalo 
Date: 2006
Persistent ID: http://hdl.handle.net/10316/4609
Origin: Estudo Geral - Universidade de Coimbra
Subject(s): First countable space; Axiom of Choice
Document details
What is a first countable space?
Description
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
Document Type
Article
Language English
Language English
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