Weakly strongly star-Menger spaces
-
Gaurav Kumar
gaurav.maths.du@gmail.com
-
Brij K. Tyagi
brijkishore.tyagi@gmail.com
Downloads
DOI:
https://doi.org/10.4067/S0719-06462021000200287Abstract
A space \(X\) is called weakly strongly star-Menger space if for each sequence (\(\mathcal{U}_{n} : n \in \omega\)) of open covers of \(X\), there is a sequence \((F_n : n\in\omega)\) of finite subsets of \(X\) such that \(\overline{\bigcup_{n\in\omega} St(F_n, \mathcal{U}_n)}\) is \(X\). In this paper, we investigate the relationship of weakly strongly star-Menger spaces with other related spaces. It is shown that a Hausdorff paracompact weakly star Menger \(P\)-space is star-Menger. We also study the images and preimages of weakly strongly star-Menger spaces under various type of maps.
Keywords
M. Bonanzinga, F. Cammaroto and Lj. D. R. KoÄinac, “Star-Hurewicz and related properties”, Appl. Gen. Topol., vol. 5, no. 1, pp. 79-89, 2004.
M. Bonanzinga, F. Cammaroto, Lj. D. R. KoÄinac and M. V. Matveev, “On weaker forms of Menger, Rothberger and Hurewicz properties”, Mat. Vesnik, vol 61, no. 1, pp. 13-23, 2019.
M. Bonanzinga and M. V. Matveev, “Some covering properties for ψ -spaces”, Mat. Vesnik, vol. 61, no. 1, pp. 3–11, 2009.
M. Bonanzinga, M. V. Matveev and B. A. Pansera, “When can a cover of a product be refined by a product of covers”, Question Answers Gen. Topology, vol. 26, no. 2, pp. 67-74, 2008.
M. Bonanzinga and B. A. Pansera, “Relative versions of some star selection principles”, Acta Math. Hungar., vol. 117, no. 3, pp. 231-243, 2007.
A. Caserta, G. M. Di Maio and Lj. D. R. KoÄinac, “Versions of properties (a) and (pp)”, Topology Appl., vol. 158, no. 12, pp. 1360–1368, 2011.
E. K. van Douwen, G. K. Reed, A. W. Roscoe and I. J. Tree, “Star covering properties”, Topology Appl., vol. 39, no. 1, pp. 71–103, 1991.
E. K. van Douwen, “The integers and topology”, in: K. Kunen, J.E. Vaughan (Eds.), Hand- book of Set-Theoretic Topology, Amsterdam: North-Holland, pp. 111–167, 1984.
R. Engelking, General Topology, Revised and completed edition, Berlin : Heldermann Verlag, 1989.
W. M. Fleischman, “A new extension of countable compactness”, Fund. Math., vol. 67, no. 1, pp. 1–9, 1971.
L. Gillman and M. Jerison, Rings of Continuous Functions, New York: Van Nostrand, 1960.
W. Just, A. W. Miller, M. Scheepers and P. J. Szeptycki, “The combinatorics of open covers II”. Topology Appl.. vol. 73, pp. 241-266, 1996.
D. Kocev, “Menger-type covering properties of topological spaces”, Filomat, vol. 29, no. 1, pp. 99–106, 2015.
D. Kocev, “Almost Menger and related spaces”, Mat. Vesnik, vol. 61, no. 2, pp. 173–180, 2009.
Lj. D. R. KoÄinac, “Star-Menger and related spaces”, Publ. Math. Debrecen, vol. 55, no. 3-4, pp. 421–431, 1999.
Lj. D. R. KoÄinac, “Star-Menger and related spaces II”, Filomat, no. 13, pp. 129–140, 1999.
Lj. D. R. KoÄinac, “Star selection principles: a survey”, Khayyam J. Math., vol. 1, no.1, pp. 82-106, 2015.
Lj. D. R. KoÄinac, “Variations of classical selection principles: An overview”, Quaest. Math., vol. 43 (2020), no.8, pp. 1121-1153, 2020.
Lj. D. R KoÄinac and C. Guido, “Relative covering properties”, Questions Answers Gen. Topology, vol. 19, no. 1, pp. 107-114, 2001.
M. V. Matveev, “Absolutely countably compact spaces”, Topology Appl., vol. 58, no.1, pp. 81–92, 1994.
M. V. Matveev, “Properties close to pseudocompactness and countable compactness”, Vestnik Moskov. Ser. I Mat. Mekh., no. 2, pp. 24-27, 1984.
M. V. Matveev, “A survey on star covering properties”, Topology Atlas (1998), Preprint No. 330.
B. A. Pansera, “Weaker forms of the Menger property”, Quaest. Math., vol. 35, no. 2, pp. 161-169, 2013.
M. Scheepers, “Combinatorics of open covers (I): Ramsey theory”, Topology Appl., vol. 69, no. 1, pp. 31-62, 1992.
Y.-K. Song, “Remarks on strongly star-Menger spaces”, Comment. Math. Univ. Carolin., vol. 54, no. 1, pp. 97–104, 2013.
Y.-K. Song, “On countable star-covering properties”, Appl. Gen. Topol., vol. 8, no. 2, pp. 249–258, 2007.
Y.-K. Song, “Absolutely strongly star-Menger spaces”, Topology Appl., vol 160, no. 3, pp. 475–481, 2013.
Y.-K. Song, “Some remarks on almost star countable spaces”, Studia Sci. Math. Hungar., vol. 52, no. 2, pp. 12–20, 2015.
L. A. Steen and J. A. Seebach, Counterexamples in Topology, New York: Dover Publications, 1995.
R. C. Walker, The Stone-ÄŒech Compactification, Ergebnisse der Mathematik und ihrer Gren- zgebiete, Band 83, New York-Berlin: Springer, 1974.
Similar Articles
- A.P. Farajzadeh, A. Amini-Harandi, D. O‘Regan, R.P. Agarwal, Strong vector equilibrium problems in topological vector spaces via KKM maps , CUBO, A Mathematical Journal: Vol. 12 No. 1 (2010): CUBO, A Mathematical Journal
- Takahiro Sudo, A covering dimension for ð¶*-algebras , CUBO, A Mathematical Journal: Vol. 8 No. 1 (2006): CUBO, A Mathematical Journal
- S. Tchuiaga, M. Koivogui, F. Balibuno, V. Mbazumutima, On topological symplectic dynamical systems , CUBO, A Mathematical Journal: Vol. 19 No. 2 (2017): CUBO, A Mathematical Journal
- Elke Wolf, Isometric weighted composition operators on weighted Banach spaces of holomorphic functions defined on the unit ball of a complex Banach space , CUBO, A Mathematical Journal: Vol. 15 No. 2 (2013): CUBO, A Mathematical Journal
- Adrian Petrus¸el, Ioan A. Rus, Marcel Adrian S¸erban, Fixed Points for Operators on Generalized Metric Spaces , CUBO, A Mathematical Journal: Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal
- Sóstenes Lins, Valdenberg Silva, On Maps with a Single Zigzag , CUBO, A Mathematical Journal: Vol. 5 No. 3 (2003): CUBO, Matemática Educacional
- K. Kalyani, N. Seshagiri Rao, Coincidence point results of nonlinear contractive mappings in partially ordered metric spaces , CUBO, A Mathematical Journal: Vol. 23 No. 2 (2021)
- K.P.R. Rao, G.N.V. Kishore, Nguyen Van Luong, A unique common coupled fixed point theorem for four maps under ψ - φ contractive condition in partial metric spaces , CUBO, A Mathematical Journal: Vol. 14 No. 3 (2012): CUBO, A Mathematical Journal
- P. Jeyanthi, P. Nalayini, T. Noiri, Pre-regular \(sp\)-open sets in topological spaces , CUBO, A Mathematical Journal: Vol. 20 No. 1 (2018)
- José Sanabria, Edumer Acosta, Carlos Carpintero, Ennis Rosas, Continuity via ΛsI-open sets , CUBO, A Mathematical Journal: Vol. 17 No. 1 (2015): CUBO, A Mathematical Journal
<< < 1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
Downloads
