Connected and disconnected fields
type: Item
instance of: scholarly article
title: Connected and disconnected fields
zbMATH Open document ID: 0635.12019
DOI: 10.1016/0166-8641(87)90056-3
author: Niel Shell
published in: Topology and its Applications
publication date: 1987-01-01T00:00:00Z
review text: The author summarizes the known results on connected and disconnected fields and adds some new results in this direction. He proposes a detailed classification of different kinds of connectedness of fields. Examples are sought of Hausdorff ring topologies on fields that are \((i)\quad arcwise\) connected; \((ii)\quad connected\) but not arcwise connected (just connected); \((iii)\quad totally\) disconnected but not ultraregular; \((iv)\quad ultraregular\) but not basically disconnected; \((v)\quad basically\) disconnected but neither a P-space nor extremally disconnected; \((vi)\quad P-spaces\); \((vii)\quad extremally\) disconnected. For a field with a ring topology, properties of F-zerosets are considered.
Mathematics Subject Classification ID: 12J99
Mathematics Subject Classification ID: 54D05
Mathematics Subject Classification ID: 54H13
Mathematics Subject Classification ID: 54G05
zbMATH DE Number: 4033874
zbMATH Keywords: connectedness of fields
zbMATH Keywords: Hausdorff ring topologies on fields
MaRDI profile type: Publication
full work available at URL: 0166-8641(87)90056-3
OpenAlex ID: W1982260929
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description: scientific article; zbMATH DE number 4033874