Remarks on Semi-Menger and Star Semi-Menger Spaces

Gaurav Kumar; Brij K.Tyagi

doi:10.2478/tmmp-2022-0003

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Remarks on Semi-Menger and Star Semi-Menger Spaces

Tatra Mountains Mathematical Publications

Volume 81 (2022): Issue 1 (November 2022)

By: Gaurav Kumar and Brij K.Tyagi

Open Access

|Nov 2022

Abstract

It is proved that for an extremally disconnected S-paracompact-T₂ spaces the properties semi-Menger, Menger, strongly star semi-Menger, strongly star-Menger, star semi-Menger, star-Menger, almost semi-Menger, almost Menger, almost star semi-Menger, almost star-Menger are equivalent. We show that a weakly semi-continuous (strongly θ-semi-continuous) image of semi-Menger (almost semi-Menger) spaces is almost semi-Menger (semi-Menger), respectively. The characterizations of semi-Menger and star semi-Menger spaces are also provided.

References

[1] AL-ZOUBI, K. Y.: S-paracompact spaces, Acta Math. Hungar. 110 (2006), 165–174.10.1007/s10474-006-0001-4
Search in Google Scholar Back to article
[2] BONANZINGA, M.—MATVEEV, M. V.: Some covering properties for ψ -Spaces,Mat. Vesnik 61 (2009), 3–11.
Search in Google Scholar Back to article
[3] CROSSLEY, S. G.—HILDEBRAND, S. K.: Semi-closure,Texas J. Sci. 22 (1971), 99–112.
Search in Google Scholar Back to article
[4] DORSETT, C.: Semi-regular spaces, Soochow J. Math. 8 (1982), 45–53.
Search in Google Scholar Back to article
[5] GILLMAN, L.—JERISON, M.: Rings of Continuous Functions, Van Nostrand, New York, 1960.10.1007/978-1-4615-7819-2
Search in Google Scholar Back to article
[6] HUREWICZ, W.: Uber die Verallgemeinerung des Borelschen Theorems,Math. Z. 24 (1926), 401–425.10.1007/BF01216792
Search in Google Scholar Back to article
[7] JANKOVIC, D.: A note on mappings of extremally disconnected spaces, Acta Math. Hungar. 46 (1985), 83–92.10.1007/BF01961010
Search in Google Scholar Back to article
[8] KOCEV, D.: Almost Menger and related spaces,Mat. vesnik 61 (2009), 173–180.
Search in Google Scholar Back to article
[9] KOČINAC, LJ. D. R.: Star-Menger and related spaces, Publ. Math. Debrecen 55 (1999), 421–431.10.5486/PMD.1999.2097
Search in Google Scholar Back to article
[10] KOČINAC, LJ. D. R.—SABAH, A.—KHAN, MOIZ UD DIN: Covering properties defined by semi-open sets,J.NonlinearSci. Appl. 9 (2016), 4388–4398.10.22436/jnsa.009.06.79
Search in Google Scholar Back to article
[11] KOČINAC, LJ. D. R.—SABAH, A.—KHAN, MOIZ UD DIN—SEBA, D.: Semi-Hurewicz spaces, Hacettepe J. Math. Stat. 46 (2017), 53–66.
Search in Google Scholar Back to article
[12] KOČINAC, LJ. D.R.: Star-Menger and related spaces, II, Filomat, 13 (1999), 129–140.
Search in Google Scholar Back to article
[13] KOČINAC, LJ. D. R.: Selected results on selection principles. In: Proceedings of the 3rd Seminar on Geometry Topology, Azarb. Univ. Tarbiat Moallem, Tabriz, Vol. 2004, (2004), pp. 71–104.
Search in Google Scholar Back to article
[14] LELEK, A.: Some cover properties of spaces, Fund. Math. 64 (1964), 209–218.10.4064/fm-64-2-209-218
Search in Google Scholar Back to article
[15] LI, Y. K.—SONG, Y-K.: Some remarks on S-paracompact spaces, Acta. Math. Hungar. 118 (2008), 345–355.10.1007/s10474-007-6225-0
Search in Google Scholar Back to article
[16] LEVINE, N.: Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36–41.10.1080/00029890.1963.11990039
Search in Google Scholar Back to article
[17] MENGER, K.: EinigeÜberdeckungssätze der Punltmengenlehre, Akademie der Wissenschaften in Wien, Mathematisch-Naturwissenschaftliche Klasse, Sitzungsberichte, Abteilung II a, Wien. Ber. 133 (1924), 421–444.
Search in Google Scholar Back to article
[18] NOIRI, T.: Properties of S-closed spaces, Acta Math. Hungar. 35 (1980), 431–436.10.1007/BF01886314
Search in Google Scholar Back to article
[19] PARVEZ, A.—KHAN MOIZ UD DIN: On nearly Menger and nearly star-Menger spaces, Filomat 33 (2019), 6219–6227.10.2298/FIL1919219A
Search in Google Scholar Back to article
[20] SAKAI, M.—SCHEEPERS, M.: The combinatorics of open covers, Recent Progress in General Topology (2014), 751–799.10.2991/978-94-6239-024-9_18
Search in Google Scholar Back to article
[21] SCHEEPERS, M.: The combinatorics of open covers (I): Ramsey theory, Topol. Appl., 69 (1996), 31–62.10.1016/0166-8641(95)00067-4
Search in Google Scholar Back to article
[22] SCHEEPERS, M.: Selection principles and covering properties in topology, Note Mat. 22 (2003), 3–41.
Search in Google Scholar Back to article
[23] SONG, Y.-K.: Remarks on strongly star-Menger spaces, Comment. Math. Univ. Carolin. 54 (2013), 97–104.
Search in Google Scholar Back to article
[24] STEEN, L. A.—SEEBACH, J. A. JR.: Counter Examples in Topology.Reprint of the 2nd ed. (1978). Dover Publications, Inc., Mineola, NY, 1995.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2022-0003 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 57 - 68

Submitted on: May 29, 2022

Published on: Nov 29, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

semi-open set,

semi-Menger space,

star semi-Menger space,

S-paracompact space

Related subjects:

Mathematics,

General mathematics

© 2022 Gaurav Kumar, Brij K.Tyagi, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 81 (2022): Issue 1 (November 2022)