Covering properties defined by semi-open sets

Volume 9, Issue 6, pp 4388--4398 http://dx.doi.org/10.22436/jnsa.009.06.79

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Authors

Amani Sabah - Department of Mathematics, COMSATS Institute of Information Technology, Chack Shahzad, Park road, Islamabad 45550, Pakistan. Moiz ud Din Khan - Department of Mathematics, COMSATS Institute of Information Technology, Chack Shahzad, Park road, Islamabad 45550, Pakistan. Ljubiša D. R. Kočinac - Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia.

Abstract

We study certain covering properties in topological spaces by using semi-open covers. A part of this article deals with Menger-type covering properties. The notions of s-Menger, almost s-Menger, star s- Menger, almost star s-Menger, strongly star s-Menger spaces are defined and corresponding properties are investigated.

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Keywords

• Semi-open set
• (star) semi-compact space
• semi-Lindelöf space
• s-Menger space
• star s-Menger space.

MSC

•  54D20
•  54C08

References

• [1] O. T. Alas, L. R. Junqueira, R. G. Wilson , Countability and star covering properties, Topology Appl., 158 (2011), 620-626.


• [2] D. R. Anderson, J. A. Jensen, Semi-continuity on topological spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci Fis. Mat. Natur., 42 (1967), 782-783.


• [3] D. Andrijević , Semi-preopen sets, Mat. Vesnik, 38 (1986), 24-32.


• [4] S.-S. Chang, Y. J. Cho, S. M. Kang , Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, New York (2001)


• [5] Y. J. Cho, M. Grabiec, V. Radu, On Nonsymmetric Topological and Probabilistic Structures, Nova Science Publishers, New York (2006)


• [6] S. G. Crossley, A note on semitopological properties, Proc. Amer. Math. Soc., 72 (1978), 409-412.


• [7] S. G. Crossley, S. K. Hildebrand , Semi-closure , Texas J. Sci., 22 (1971), 99-112.


• [8] S. G. Crossley, S. K. Hildebrand, Semi-topological properties, Fund. Math., 74 (1972), 233-254.


• [9] G. Di Maio, T. Noiri , On s-closed spaces, Indian J. Pure Appl. Math., 18 (1987), 226-233.


• [10] G. Di Maio, T. Noiri, Weak and strong forms of irresolute functions, Rend. Circ. Mat. Palermo(2). Suppl., 18 (1988), 255-273.


• [11] C. Dorsett , Semi compactness, semi separation axioms, and product spaces, Bull. Malaysian Math. Soc., 4 (1981), 21-28.


• [12] C. Dorsett , Semi-regular spaces, Soochow J. Math., 8 (1982), 45-53.


• [13] R. Engelking, General Topology, Heldermann Verlag, Berlin (1989)


• [14] M. Ganster, On covering properties and generalized open sets in topological spaces, Math. Chronicle, 19 (1990), 27-33.


• [15] M. Ganster, D. S. Janković, I. L. Reilly, On compactenss with respect to semi-open sets, Comment. Math. Univ. Carolonae, 31 (1990), 37-39.


• [16] W. Hurewicz , Über die Verallgemeinerung des Borelschen Theorems, Math. Z., 24 (1926), 401-425.


• [17] D. Kocev , Almost Menger and related spaces , Mat. Vesnik, 61 (2009), 173-180


• [18] Lj. D. R. Kočinac, Star-Menger and related spaces, Publ. Math. Debrecen, 55 (1999), 421-431.


• [19] Lj. D. R. Kočinac , Star-Menger and related spaces, II., Filomat, 13 (1999), 129-140.


• [20] Lj. D. R. Kočinac, Selected results on selection principles, Proceedings of the 3rd Seminar on Geometry & Topology, Azarb. Univ. Tarbiat Moallem, Tabriz, 2004 (2004), 71-104.


• [21] Lj. D. R. Kočinac, Star selection principles: A survey, Khayyam J. Math., 1 (2015), 82-106.


• [22] K. Kunen, Luzin spaces, Topology Proc., 1 (1976), 191-199.


• [23] N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.


• [24] S. N. Maheswari, R. Prasad, On s-regular spaces, Glasnik Mat. Ser., 10 (1975), 347-350.


• [25] M. V. Matveev, A survey on star covering properties, Topology Atlas, Preprint No. 330 (1998)


• [26] M. V. Matveev , On the extent of SSM spaces, preprint, (1998)


• [27] K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Stzungsberischte Abt. 3a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik, 133 (1924), 421-444.


• [28] M. Sakai, Star versions of the Menger property, Topology Appl., 176 (2014), 22-34.


• [29] M. Sakai, M. Scheepers, The combinatorics of open covers, Recent progress in general topology, 2014 (2014), 751-799.


• [30] M. Scheepers , Combinatorics of open covers, I, Ramsey theory, Topology Appl., 69 (1996), 31-62.


• [31] M. Scheepers, Selection principles and covering properties in Topology, Note Mat., 22 (2003), 3-41.


• [32] Y.-K. Song, Remarks on strongly star-Menger spaces, Comment. Math. Univ. Carolin., 54 (2013), 97-104.


• [33] Y.-K. Song , Remarks on star-Menger spaces, Houston J. Math., 40 (2014), 917-925.


• [34] T. Thompson, S-closed spaces, Proc. Amer. Math. Soc., 60 (1976), 335-338.


• [35] B. Tsaban, Some new directions in infinite-combinatoril topology, Set Theory, Trends in Mathematics, Birkhäuser, Basel, 2006 (2006), 225-255.


• [36] B. Tsaban, Combinatorial aspects of selective star covering properties in \(\Psi\)-spaces, Topology Appl., 192 (2015), 198-207.


• [37] E. K. Van Douwen, G. M. Reed, A. W. Roscoe, I. J. Tree , Star covering properties , Topology Appl., 39 (1991), 71-103.