Browse > Article
http://dx.doi.org/10.4134/CKMS.c200455

INFRA-TOPOLOGIES REVISITED: LOGIC AND CLARIFICATION OF BASIC NOTIONS  

Witczak, Tomasz (Institute of Mathematics University of Silesia)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 279-292 More about this Journal
Abstract
In this paper we adhere to the definition of infra-topological space as it was introduced by Al-Odhari. Namely, we speak about families of subsets which contain ∅ and the whole universe X, being at the same time closed under finite intersections (but not necessarily under arbitrary or even finite unions). This slight modification allows us to distinguish between new classes of subsets (infra-open, ps-infra-open and i-genuine). Analogous notions are discussed in the language of closures. The class of minimal infra-open sets is studied too, as well as the idea of generalized infra-spaces. Finally, we obtain characterization of infra-spaces in terms of modal logic, using some of the notions introduced above.
Keywords
Generalized topological spaces; infra-topological spaces; modal logic;
Citations & Related Records
연도 인용수 순위
  • Reference
1 F. El Khoury, Iris Biometric Model for Secured Network Access, CRC Press, Taylor & Francis Group 2017, pp. 37-41.
2 R. Jamunarani, P. Jeyanthi, and T. Noiri, On generalized weak structures, J. Algorithm Comput. 47 (2016), 21-26.
3 E. Korczak-Kubiak, A. Loranty, and R. J. Pawlak, Baire generalized topological spaces, generalized metric spaces and infinite games, Acta Math. Hungar. 140 (2013), no. 3, 203-231. https://doi.org/10.1007/s10474-013-0304-1   DOI
4 E. Pacuit, Neighborhood Semantics for Modal Logic, Short Textbooks in Logic, Springer, Cham, 2017. https://doi.org/10.1007/978-3-319-67149-9   DOI
5 R. J. Pawlak and A. Loranty, The generalized entropy in the generalized topological spaces, Topology Appl. 159 (2012), no. 7, 1734-1742. https://doi.org/10.1016/j.topol.2011.05.043   DOI
6 A. Piekosz, Generalizations of topological spaces, https://www.researchgate.net/publication/314392123_Generalizations_of_Topological_Spaces.
7 T. Witczak, Generalized topological semantics for weak modal logics, https://arxiv.org/pdf/1904.06099.pdf.
8 T. Witczak, Intuitionistic modal logic based on neighborhood semantics without superset axiom, https://arxiv.org/pdf/1707.03859.pdf.
9 A. M. Al-Odhari, I-continuous functions and I*-continuous functions on infra topological spaces, Int. J. Math. Archive 7 (2016), no. 3, 18-22.
10 J. Avila and F. Molina, Generalized weak structures, Int. Math. Forum 7 (2012), no. 49-52, 2589-2595.
11 S. Chakrabarti and H. Dasgupta, Infra-topological space and its applications, Rev. Bull. Calcutta Math. Soc. 17 (2009), no. 1-2, 13-22.
12 V. Popa and T. Noiri, On M-continuous functions, Anal. Univ. "Dunarea de Jos" Galati, Ser. Mat. Fiz. Mecan. Teor. Fasc. II 18 (2000), no. 23, 31-41.
13 H. Soldano, A modal view on abstract learning and reasoning, Ninth Symposium on Abstraction, Reformulation, and Approximation, SARA 2011. https://bioinfo.mnhn.fr/abi/people/soldano/draftSARA2011.pdf.
14 K. Vaiyomathi and F. Nirmala Irudayam, Infra generalized b-closed sets in infratopological space, Int. J. Math. Trends Technology 47 (2017), no. 1, 56-65.   DOI
15 S. Dhanalakshmi and R. Malini Devi, On generalized regular infra-closed sets, Int. J. Math. Archive 7 (2016), no. 8, 33-36.
16 R. Seethalakshmi and M. Kamaraj, Extension of binary topology, Int. J. Comput. Sci. Engineering 7 (2019), no. 5, 194-197. https://doi.org/10.26438/ijcse/v7si5.194197   DOI
17 A. M. Al-Odhari, On infra-topological spaces, Int. J. Math. Archive 6 (2015), no. 11, 179-184.
18 C. Carpintero, E. Rosas, M. Salas-Brown, and J. Sanabria, Minimal open sets on generalized topological space, Proyecciones 36 (2017), no. 4, 739-751. https://doi.org/10.4067/s0716-09172017000400739   DOI
19 S. Chakrabarti and H. Dasgupta, Touching sets and its applications, Int. J. Math. Anal. 8 (2014), no. 52, 2577-2589.   DOI
20 G. Choquet, Convergences, Ann. Univ. Grenoble. Sect. Sci. Math. Phys. (N.S.) 23 (1948), 57-112.
21 M. Bozic and K. Dosen, Models for normal intuitionistic modal logics, Studia Logica 43 (1984), no. 3, 217-245. https://doi.org/10.1007/BF02429840   DOI
22 Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351-357. https://doi.org/10.1023/A:1019713018007   DOI
23 A. S. Mashhour, A. A. Allam, F. S. Mahmoud, and F. H. Khedr, On supratopological spaces, Indian J. Pure Appl. Math. 14 (1983), no. 4, 502-510.