Abstract
In the paper we concentrate on a generalized topological space generated by a density type operator on a measurable space. The properties of such generalized topological space are investigated. Moreover, the properties of nowhere dense sets, meager sets and compact sets in this generalized topological space are studied.
Keywords
a generalized topological space separation axioms a nowhere dense set the lower density operator
References
- [1] Á. Császár, Generalized open sets, Acta Math. Hungar. 75, 65-87, 1997.
- [2] Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (4), 351-357, 2002.
- [3] Á. Császár, γ-connected sets, Acta Math. Hungar. 101 (4), 273-279, 2003.
- [4] Á. Császár, Separation axioms for generalized topologies, Acta Math. Hungar. 104 (1-2), 63-69, 2004.
- [5] O. Haupt and C. Pauc, La topologie de Denjoy envisagée comme vraie topologie, C. R. Acad. Sci. Paris 234, 390-392, 1952.
- [6] J. Hejduk, S. Lindner and A. Loranty, On lower density type operators and topologies generated by them, Filomat 32 (14), 4949-4957, 2018.
- [7] J. Hejduk and R. Wiertelak, On the abstract of density topologies generated by lower and almost lower density operators, Traditional and present-day topics in real analysis, University of Łódź, 431-440, 2013.
- [8] T. Jyothis and J.J. Sunil, μ-Compactness in Generalized Topological Spaces, J. Adv. Stud. Topol. 3 (3), 18-22, 2012.
- [9] E. Korczak-Kubiak, A. Loranty and R.J. Pawlak, Baire generalized topological spaces, generalized metric spaces and infinite games, Acta Math. Hungar. 140 (3), 203-231, 2013.
- [10] S. Lindner and M. Terepeta, On the Position of Abstract Density Topologies in the Lattice of All Topologies, Filomat 30 (2), 281-286, 2016.
- [11] J. Lukeš, J. Malý and L. Zajíček, Fine topology methods, Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer-Verlag, Berlin, 1986.
- [12] J. Oxtoby, Measure and Category, Springer-Verlag, New York, 1987.
- [13] W. Wilczyński, Density topologies, Handbook of Measure Theory, Ed. E. Pap. Elsevier, chapter 15, 675-702, 2002.
Abstract
References
- [1] Á. Császár, Generalized open sets, Acta Math. Hungar. 75, 65-87, 1997.
- [2] Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (4), 351-357, 2002.
- [3] Á. Császár, γ-connected sets, Acta Math. Hungar. 101 (4), 273-279, 2003.
- [4] Á. Császár, Separation axioms for generalized topologies, Acta Math. Hungar. 104 (1-2), 63-69, 2004.
- [5] O. Haupt and C. Pauc, La topologie de Denjoy envisagée comme vraie topologie, C. R. Acad. Sci. Paris 234, 390-392, 1952.
- [6] J. Hejduk, S. Lindner and A. Loranty, On lower density type operators and topologies generated by them, Filomat 32 (14), 4949-4957, 2018.
- [7] J. Hejduk and R. Wiertelak, On the abstract of density topologies generated by lower and almost lower density operators, Traditional and present-day topics in real analysis, University of Łódź, 431-440, 2013.
- [8] T. Jyothis and J.J. Sunil, μ-Compactness in Generalized Topological Spaces, J. Adv. Stud. Topol. 3 (3), 18-22, 2012.
- [9] E. Korczak-Kubiak, A. Loranty and R.J. Pawlak, Baire generalized topological spaces, generalized metric spaces and infinite games, Acta Math. Hungar. 140 (3), 203-231, 2013.
- [10] S. Lindner and M. Terepeta, On the Position of Abstract Density Topologies in the Lattice of All Topologies, Filomat 30 (2), 281-286, 2016.
- [11] J. Lukeš, J. Malý and L. Zajíček, Fine topology methods, Real Analysis and Potential Theory, Lecture Notes in Math. 1189, Springer-Verlag, Berlin, 1986.
- [12] J. Oxtoby, Measure and Category, Springer-Verlag, New York, 1987.
- [13] W. Wilczyński, Density topologies, Handbook of Measure Theory, Ed. E. Pap. Elsevier, chapter 15, 675-702, 2002.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | December 8, 2020 |
| Published in Issue | Year 2020 Volume: 49 Issue: 6 |