Topological connectednesses and congruences

Stefan Veldsman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

It is known that the connectednesses of topological spaces in the sense of Preuß is the topological analogue of the Kurosh-Amistsur radicals of algebraic structures in a categorical sense. Here this connection is further explored. As in universal algebra, a congruence on a topological space has been defined. It is shown that a connectedness can be characterized in terms of conditions on congruences which are the precise topological analogues of those conditions that characterize the radical classes of rings in terms of ideals.

Original languageEnglish
Pages (from-to)1757-1772
Number of pages16
JournalQuaestiones Mathematicae
Volume44
Issue number12
DOIs
Publication statusPublished - 2021
Externally publishedYes

Keywords

  • connectedness
  • disconnectedness
  • radical class
  • topological congruence
  • Topological space

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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