Categorically-algebraic topology and its applications

J 2015

Categorically-algebraic topology and its applications

SOLOVJOVS, Sergejs

Základní údaje

Originální název

Categorically-algebraic topology and its applications

Autoři

SOLOVJOVS, Sergejs

Vydání

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

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Írán

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.381

Organizační jednotka

Přírodovědecká fakulta

DOI

http://dx.doi.org/10.22111/IJFS.2015.2020

UT WoS

000358110900005

Klíčová slova anglicky

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

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 6. 3. 2020 09:39, Mgr. Marie Šípková, DiS.

Anotace

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.

Citovat

SOLOVJOVS, Sergejs. Categorically-algebraic topology and its applications. Iranian Journal of Fuzzy Systems. Iran, 2015, roč. 12, č. 3, s. 57-94. ISSN 1735-0654. Dostupné z: https://dx.doi.org/10.22111/IJFS.2015.2020.

@article{1311735,
   author = {Solovjovs, Sergejs},
   article_location = {Iran},
   article_number = {3},
   doi = {http://dx.doi.org/10.22111/IJFS.2015.2020},
   keywords = {Categorically-algebraic topology; Lattice-valued topology; Soft topology; Topological category; Topological system; Topological theory},
   language = {eng},
   issn = {1735-0654},
   journal = {Iranian Journal of Fuzzy Systems},
   note = {žádný z autorů nemá na WoS afiliaci na MU, nelze tedy výsledek přenášet do RIV!},
   title = {Categorically-algebraic topology and its applications},
   url = {http://ijfs.usb.ac.ir/article_2020.html},
   volume = {12},
   year = {2015}
}

TY  - JOUR
ID  - 1311735
AU  - Solovjovs, Sergejs
PY  - 2015
TI  - Categorically-algebraic topology and its applications
JF  - Iranian Journal of Fuzzy Systems
VL  - 12
IS  - 3
SP  - 57-94
EP  - 57-94
SN  - 17350654
N1  - žádný z autorů nemá na WoS afiliaci na MU, nelze tedy výsledek přenášet do RIV!
KW  - Categorically-algebraic topology
KW  - Lattice-valued topology
KW  - Soft topology
KW  - Topological category
KW  - Topological system
KW  - Topological theory
UR  - http://ijfs.usb.ac.ir/article_2020.html
N2  - 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.
ER  -

SOLOVJOVS, Sergejs. Categorically-algebraic topology and its applications. \textit{Iranian Journal of Fuzzy Systems}. Iran, 2015, roč.~12, č.~3, s.~57-94. ISSN~1735-0654. Dostupné z: https://dx.doi.org/10.22111/IJFS.2015.2020.

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