J 2015

Categorically-algebraic topology and its applications

SOLOVJOVS, Sergejs

Basic information

Original name

Categorically-algebraic topology and its applications

Authors

SOLOVJOVS, Sergejs

Edition

Iranian Journal of Fuzzy Systems, Iran, 2015, 1735-0654

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Islamic Republic of Iran

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Impact factor

Impact factor: 0.381

Organization unit

Faculty of Science

DOI

UT WoS

000358110900005

Keywords in English

Categorically-algebraic topology; Lattice-valued topology; Soft topology; Topological category; Topological system; Topological theory

Tags

Tags

International impact, Reviewed
Změněno: 6/3/2020 09:39, Mgr. Marie Šípková, DiS.

Abstract

V originále

This paper introduces a new approach to topology, based in category theory and universal algebra, and called categorically-algebraic (catalg) topology. It incorporates the most important settings of lattice-valued topology, including poslat topology of S. E. Rodabaugh, (L,M)-fuzzy topology of T. Kubiak and A. Sostak, and M-fuzzy topology on L-fuzzy sets of C. Guido. Moreover, its respective categories of topological structures are topological over their ground categories. The theory also extends the notion of topological system of S. Vickers (and its numerous many-valued modifications of J. T. Denniston, A. Melton and S. E. Rodabaugh), and shows that the categories of catalg topological structures are isomorphic to coreflective subcategories of the categories of catalg topological systems. This extension initiates a new approach to soft topology, induced by the concept of soft set of D. Molodtsov, and currently pursued by various researchers.