Star-Hurewicz and related properties

Maddalena Bonanzinga, F. Cammaroto, Ljubisa D.R. Kocinac


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.


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

Full Text:



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.

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

J. Gerlits and Zs. Nagy, Some properties of C(X), I, Topology Appl. 14 (1982), 151-161.

W. Hurewicz, Über eine Verallgemeinerung des Borelschen Theorems, Math. Z. 24 (1925), 401-421.

W. Hurewicz, Über Folgen stetiger Funktionen, Fund. Math. 9 (1927), 193-204.

W. Just, A.W. Miller, M. Scheepers and P.J. Szeptycki, The combinatorics of open covers II, Topology Appl. 73 (1996), 241-266.

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.

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.

F. Rothberger, Eine Verschärfung der Eigenschaft C, Fund. Math. 30 (1938), 50-55.

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

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM


Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. Star versions of the Rothberger property on hyperspaces
Javier Casas-de la Rosa, Iván Martínez-Ruiz, Alejandro Ramírez-Páramo
Topology and its Applications  vol: 283  first page: 107396  year: 2020  
doi: 10.1016/j.topol.2020.107396

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147