Bitopological and algebraic structures in the context of Baire-type properties and generalized Boolean algebras
type: Item
instance of: scholarly article
title: Bitopological and algebraic structures in the context of Baire-type properties and generalized Boolean algebras
zbMATH Open document ID: 1005.54032
DOI: 10.1023/A:1015849909851
published in: Journal of Mathematical Sciences (New York)
publication date: 2003-02-27T00:00:00Z
review text: The present paper consists of four sections, the first of which is devoted to the investigation of some necessary facts from the theory of bitopological spaces and general topology. In the second section the author deals with different bitopological types of Baire spaces. He introduces and studies the so-called Baire-type properties of bitopological spaces and their applications. In Section 3, the Baire-type properties are used to enrich the information on a fine-topology both in analysis and potential theory. Also, the author offers some other results drawing a parallel between the potential and bitopological spaces theories. In the fourth section the author, observing that the development of the theory of bitopological spaces forms the base for introducing a new kind of algebra, called generalized Boolean algebra, continues and refines the research on such algebras. Also, he discusses the bitopological modification of Stone's representation theorem. This last section is an interesting attempt to connect a bitopological structure with a generalized algebraic one.
Mathematics Subject Classification ID: 54E55
Mathematics Subject Classification ID: 06E99
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 1821711
zbMATH Keywords: set of \((i,j)\)-category
zbMATH Keywords: \((i,j)\)-Baire space
zbMATH Keywords: generalized Boolean algebra
zbMATH Keywords: Stone's representation theorem
author: Badri P. Dvalishvili
reviewed by: Chariklia Konstadilaki
MaRDI profile type: Publication
full work available at URL: a:1015849909851
OpenAlex ID: W252043047
Recommended article: Q3428407
Recommended article: Q3786510
Recommended article: Q3752435
Recommended article: Q4133677
Recommended article: Q3994002
Recommended article: On axiomatizations of Boolean algebras
Recommended article: Q3689231
Recommended article: Q4654003
Recommended article: Q4249730
Recommended article: On BPI Restricted to Boolean Algebras of Size Continuum
description: scientific article; zbMATH DE number 1821711