On Semi-Open Sets and Mutual Correspondence Between Properties of Functions Considered with Respect to Different Topological Structures

Ewa Korczak-Kubiak; Ryszard J. Pawlak

doi:10.1515/tmmp-2016-0010

.blurhash-client-img { display: none !important; }

On Semi-Open Sets and Mutual Correspondence Between Properties of Functions Considered with Respect to Different Topological Structures

Tatra Mountains Mathematical Publications

Volume 65 (2016): Issue 1 (March 2016)

By: Ewa Korczak-Kubiak and Ryszard J. Pawlak

Open Access

|Aug 2016

Abstract

At the end of the twentieth century, Á. Császár pointed out the possibility of the transition from topology to generalized topology and vice versa. One of the tools used for this purpose are semi-open sets. In this paper, we investigate properties of functions in GTS in the context of semi-open sets, and problems connected with transfer of properties of functions defined and assuming their values in primal spaces to functions considered as mappings in the spaces generated by primal spaces.

References

[1] ABDUL-JABBAR, A. M.: Topological property of θ-semi-open sets, Int. J. Pure AppL Sci Technol. 13 (2012), 7-15.
Search in Google Scholar
[2] ALSEDA, L. LLIBRE, J.-MISIUREWICZ, M.: Combinatorial Dynamics and Entropy in Dimension One. World Scientific Publ., Singapore, 1993.10.1142/1980
Search in Google Scholar
[3] BAYHAN, S.-KANIBIR, A.-REILLY, I. L.: On functions between generalized topological spaces, Appl. Gen. Topol. 14 (2013), 195-203.10.4995/agt.2013.1588
Search in Google Scholar
[4] BENCHALLI, S. S.-WALI, R. S.: On RW-closed sets in topological spaces, Bull. Malays. Math. Sci. Soc. (2) 30 (2007), 99-110.
Search in Google Scholar
[5] BRUCKNER, A. M. - HU, T.: On scrambled sets for chaotic functions, Trans. Amer. Math. Soc. 301 (1987), 289-297.10.1090/S0002-9947-1987-0879574-0
Search in Google Scholar
[6] CALDAS, M.-SARAF, R. K.: On approximately semiopen maps in topological spaces, Divulg. Mat. 14 (2006), 31-37.
Search in Google Scholar
[7] CSÁSZÁR, A.: Generalized open sets, Acta Math. Hungar. 75 (1997), 65-87.10.1023/A:1006582718102
Search in Google Scholar
[8] CSÁSZÁR, A.: Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), 351-357.10.1023/A:1019713018007
Search in Google Scholar
[9] CSÁSZÁR, A.: Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), 53-66.10.1007/s10474-005-0005-5
Search in Google Scholar
[10] CSÁSZÁR, A.: Weak structures, Acta Math. Hungar. 131 (2011), 193-195.10.1007/s10474-010-0020-z
Search in Google Scholar
[11] EKICI, E.-JAFARI S.: On a weaker form of complete irresoluteness, BoL Soc. Paran. Mat. 26 (2008), 81-87.
Search in Google Scholar
[12] EKICI, E.: Further new generalized topologies via mixed constructions due to Császár, Math. Bohem. 140 (2015), 1-9. 10.21136/MB.2015.144173
Search in Google Scholar
[13] ENGELKING, R.: General Topology. Heldermann, Berlin, 1989.
Search in Google Scholar
[14] GENE CROSSLEY, S.-HILDEBRAND, S. K.: Semi-topological properties, Fund. Math. 74 (1972), 233-254.10.4064/fm-74-3-233-254
Search in Google Scholar
[15] GOTTSCHALK, W. H.-HEDLUND, G. A.: Topological Dynamics, in: Amer. Math. Soc. Colloq. Publ., Vol 36, Providence, RI, 1995.
Search in Google Scholar
[16] KALAlYANL N.-SAI SUNDARA KRISHNAN, G.: On γ-generalized α-continuous mappings in topological spaces, Bonfring Int. J. Data Mining 2 (2012), 23-27.10.9756/BIJDM.1108
Search in Google Scholar
[17] KOLYADA, S.-SNOHA, L'.: Some aspects of topological transitivity-a survey. Grazer Math. Ber. 334 (1997), 3-35.
Search in Google Scholar
[18] KORCZAK-KUBIAK, E-LORANTY, A.-PAWLAK, R. J.: Baire generalized topological spaces, generalized metric spaces and infinite games. Acta Math. Hung. 140 (2013), 203-231.
Search in Google Scholar
[19] LI, J.: Generalized topologies generated by subbases Acta Math. Hung. 114 (2007), 1-12.
Search in Google Scholar
[20] LORANTY, A.-PAWLAK, R. J.: On the transitivity of multifunctions and density of orbits in generalized topological spaces. Acta Math. Hungar. 135 (2012), 56-66.
Search in Google Scholar
[21] MAI, J. H.-SUN, W. H.: Transitivities of maps of general topological spaces, Topology Appl. 157 (2010), 946-953.10.1016/j.topol.2009.12.011
Search in Google Scholar
[22] DE MELO, W.-VAN STRIEN, S.: One-Dimensional Dynamics. Springer, Berlin, 1993.10.1007/978-3-642-78043-1
Search in Google Scholar
[23] MICHAEL, F. I.: On semi-open sets with respect to an ideal, Eur. J. Pure Appl. Math. 6 (2013), 53-58.
Search in Google Scholar
[24] PETERSEN, K.: Ergodic Theory, in: Cambridge Stud. Adv. Math., Vol. 2, Cambridge Univ. Press, Cambridge, 1983.
Search in Google Scholar
[25] POWAR, P. L.-RAJAK, K. L.: Some new concepts of continuity in generalized topological space, Int. J. Comput. Appl. 38 (2012), 12-17.
Search in Google Scholar
[26] SIDOROV, Y. A.: Topologically indecomposable, transformations of the n-dimensional- space, Volzh. Mat. Sbornik 5 (1966), 326-330. (In Russian)
Search in Google Scholar
[27] WALTERS, P.: An Introduction to Ergodic Theory. Springer, New York, 1982.10.1007/978-1-4612-5775-2
Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.1515/tmmp-2016-0010 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

Journal RSS Feed

Language: English

Page range: 119 - 134

Submitted on: Nov 12, 2015

Published on: Aug 4, 2016

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

semi-open set,

generalized topological space,

Baire generalized topological space,

Related subjects:

© 2016 Ewa Korczak-Kubiak, Ryszard J. Pawlak, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 65 (2016): Issue 1 (March 2016)