Disasters in topology without the axiom of choice
type: Item
instance of: scholarly article
title: Disasters in topology without the axiom of choice
zbMATH Open document ID: 1027.03040
author: Kyriakos Keremedis
published in: Archive for Mathematical Logic
publication date: 2003-09-16T00:00:00Z
review text: The author shows that some well-known theorems of topology which are proved in ZFC (e.g., (1) Countable products of metrizable spaces are metrizable. (2) Countable products of second countable spaces are second countable. (3) Countable products of first countable spaces are first countable. (4) Countable products of separable \(T_2\) spaces are separable.) are not provable in ZF\(^-\) without AC. However, the countable axiom of choice CAC implies each of (2) and (4), and the countable multiple choice axiom CMC implies (1) and (3).
Mathematics Subject Classification ID: 03E25
Mathematics Subject Classification ID: 54A35
Mathematics Subject Classification ID: 54D30
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 1982449
zbMATH Keywords: axiom of choice AC
zbMATH Keywords: countable axiom of choice CAC
zbMATH Keywords: countable axiom of multiple choice CMC
zbMATH Keywords: separable
zbMATH Keywords: compact
zbMATH Keywords: countably compact
zbMATH Keywords: first countable
zbMATH Keywords: metrizable
reviewed by: Tomasz Natkaniec
MaRDI profile type: Publication
full work available at URL: s001530100094
OpenAlex ID: W2017523153
Wikidata QID: Q114018325
DOI: 10.1007/S001530100094
description: scientific article; zbMATH DE number 1982449