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@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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