Star-Hurewicz and related properties

Maddalena Bonanzinga

Italy

University of Messina

Department of Mathematics

F. Cammaroto

Italy

University of Messina

Department of Mathematics

Ljubisa D.R. Kocinac

Serbia

University of Nis

Faculty of Sciences and Mathematics
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Accepted: 2013-12-02

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DOI: https://doi.org/10.4995/agt.2004.1996
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Keywords:

Selection principles, (strongly) star-Menger, (strongly) star-Rothberger, (strongly) star-Hurewicz, Groupability, Weak groupability, ω-cover

Supporting agencies:

MURST - PRA 2000. MSRS

grant N0 1233

Abstract:

We continue the investigation of star selection principles first considered. We are concentrated onto star versions of the Hurewicz covering property and star selection principles related to the classes of open covers which have been recently introduced.

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References:

L. Babinkostova, Lj.D.R. Kocinac and M. Scheepers, Combinatorics of open covers (VIII), Topology Appl. (to appear).

M. Bonanzinga, Star-Lindelöf and absolutely star-Lindelöf spaces, Q & A in Gen. Topology 16 (1998), 79-104.

E.K. van Douwen, G.M. Reed, A.W. Roscoe and I.J. Tree, Star covering properties, Topology Appl. 39 (1991), 71-103. https://doi.org/10.1016/0166-8641(91)90077-Y

R. Engelking, General Topology (PWN, Warszawa, 1977).

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

W. Just, A.W. Miller, M. Scheepers and P.J. Szeptycki, The combinatorics of open covers II, Topology Appl. 73 (1996), 241-266. https://doi.org/10.1016/S0166-8641(96)00075-2

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

Lj.D.R. Kocinac, Selection principles in uniform spaces, Note di Matematica (to appear).

Lj.D.R. 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.V. Matveev, On properties similar to countable compactness and pseudocompactness, Vestnik MGU, Ser. Mat. Mekh., (1984), N0 2, 24-27 (in Russian).

M.V. Matveev, A survey on star covering properties, Topology Atlas, Preprint N0 330, 1998.

M.V. Matveev, On the extent of SSM spaces, preprint.

K. Menger, Einige Überdeckungssätze der Punktmengenlehre, Sitzungsberischte Abt. 2a, Mathematik, Astronomie, Physik, Meteorologie und Mechanik (Wiener Akademie, Wien) 133 (1924), 421-444.

A.W. Miller and D.H. Fremlin, On some properties of Hurewicz, Menger and Rothberger, Fund. Math. 129 (1988), 17-33. https://doi.org/10.4064/fm-129-1-17-33

F. Rothberger, Eine Verschärfung der Eigenschaft C, Fund. Math. 30 (1938), 50-55. https://doi.org/10.4064/fm-30-1-50-55

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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