Alexandroff duplicate and  βκ

Andrzej A Szymanski

doi:10.4995/agt.2022.15586

Authors

Andrzej A Szymanski Slippery Rock University of Pennsylvania https://orcid.org/0000-0002-6992-8953

DOI:

https://doi.org/10.4995/agt.2022.15586

Keywords:

extremally disconnected, ultrafilter space

Abstract

We discuss spaces and the Alexandroff duplicates of those spaces that admit a Č-S embedding into the Čech-Stone compactification of a discrete space.

Downloads

Download data is not yet available.

Author Biography

Andrzej A Szymanski, Slippery Rock University of Pennsylvania

Department of Mathematics and Statistics

References

P. S. Alexandroff and P. S. Urysohn, Memoire sur les espaces topologiques compacts, Verh. Kon. Akad.Wetensch. Naturkunde. 14, Amsterdam, 1929.

K. Almontashery and L. Kalantan, Results about the Alexandroff duplicate space, Appl. Gen. Topol. 17, no. 2 (2016), 117-122. https://doi.org/10.4995/agt.2016.4521

P. Bhattacharjee, M. Knox and W. McGovern, Disconnection in the Alexandroff duplicate, Appl. Gen. Topol. 22, no. 2 (2021), 331-344. https://doi.org/10.4995/agt.2021.14602

A. Błaszczyk and M. Tkachenko, Transversal, T_{1}-$independent, and $T_{1}-$complementary topologies, Topology and Its Applications 230 (2017), 308-337. https://doi.org/10.1016/j.topol.2017.08.018

A. Błaszczyk and M. Tkachenko, Transversal, T_{1}-$independent, and the Alexandroff duplicate, Topology and Its Applications 159 (2012), 75-87. https://doi.org/10.1016/j.topol.2011.07.023

A. Caserta, G. Di Maio and L. Kocinac, Versions of properties (a) and (pp), Topology and Its Applications 158 (2011), 1360-1368. https://doi.org/10.1016/j.topol.2011.05.010

A. Caserta and S. Watson, The Alexandroff duplicate and its subspaces, Applied General Topology 8 (2007), 187-205. https://doi.org/10.4995/agt.2007.1880

R. E. Chandler, G. D. Faulkner, J. P. Guglielmi and M. C. Memory, Generalizing the Alexandroff-Urysohn double circumference construction, Proc. Amer. Math. Soc. 83, no. 3 (1981), 606-608. https://doi.org/10.1090/S0002-9939-1981-0627703-6

E. van Douwen, Applications of maximal topologies, Topology and its Applications 51 (1993), 125-139. https://doi.org/10.1016/0166-8641(93)90145-4

A. Dow, Two to one images and PFA, Israel J. Math. 156 (2006), 221-241. https://doi.org/10.1007/BF02773833

A. Dow, On van Douwen spaces and retracts of $beta N $, Mathematica Bohemica 132, no. 4 (2007), 345-368. https://doi.org/10.21136/MB.2007.133962

R. Engelking, On the double circumference of Alexandroff, Bull. Acad. Pol. Sci. Ser. Math. 16 (1968), 629-634.

R. Engelking, General topology, Sigma series in pure mathematics, Vol. 6, Berlin, Heldermann, 1989.

S. García-Ferreira and C. Yescas-Aparicio, Families of retractions and families of closed subsets on compact spaces, Topology and its Applications 301 (2021): 107504. https://doi.org/10.1016/j.topol.2020.107504

E. Hewitt, A problem of set-theoretic topology, Duke J. Math. 10 (1943), 309-333. https://doi.org/10.1215/S0012-7094-43-01029-4

I. Juhasz and S. Mrowka, E-compactness and the Alexandroff duplicate, Indagationes Math. 73 (1970), 26-29. https://doi.org/10.1016/S1385-7258(70)80004-X

M. Katĕtov, On spaces which do not have disjoint dense subspaces, Mat Sb. 21 (1947), 3-12.