Counterexample of theorems on star versions of Hurewicz property

Manoj Bhardwaj

India

University of Delhi

Department of Mathematics

Submitted: 2019-06-12

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Accepted: 2019-11-24

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Published: 2020-04-03

DOI: https://doi.org/10.4995/agt.2020.11976
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Keywords:

Hurewicz spac, star-Hurewicz space, strongly star-Hurewicz space

Supporting agencies:

University Grants Commission

India

Abstract:

In this paper, an example contradicting Theorem 4.5 and Theorem 5.3 is provided and these theorems are proved under some extra  hypothesis.
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References:

M. Bonanzinga, F. Cammaroto and Lj. D. R. Kocinac, Star-Hurewicz and related properties, Appl. Gen. Topol. 5, no. 1 (2004), 79-89. https://doi.org/10.4995/agt.2004.1996

R. Engelking, General Topology, Revised and completed edition, Heldermann Verlag Berlin (1989).

J. Gerlits and Zs. Nagy, Some properties of $C(X), I$, Topology Appl. 14 (1982), 151-161. https://doi.org/10.1016/0166-8641(82)90065-7

W. Hurewicz, Über eine verallgemeinerung des Borelschen Theorems, Math. Z. 24 (1925), 401-421. https://doi.org/10.1007/BF01216792

W. Hurewicz, Über Folgen stetiger Funktionen, Fund. Math. 9 (1927), 193-204. https://doi.org/10.4064/fm-9-1-193-210

Lj. D. Kocinac, Star-Menger and related spaces, Publ. Math. Debrecen 55 (1999), 421-431.

Lj. D. Kocinac and M. Scheepers, Combinatorics of open covers (VII): Groupability, Fund. Math. 179 (2003), 131-155. https://doi.org/10.4064/fm179-2-2

M. Scheepers, Combinatorics of open covers (I) : Ramsey theory, Topology Appl. 69 (1996), 31-62. https://doi.org/10.1016/0166-8641(95)00067-4

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