Bitopological and algebraic structures in the context of Baire-type properties and generalized Boolean algebras
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.
scientific article; zbMATH DE number 1821711