A disjointly tight irresolvable space

Angelo Bella; Michael Hrusak

doi:10.4995/agt.2020.13836

Authors

Angelo Bella University of Catania
Michael Hrusak Universidad Nacional Autónoma de México

DOI:

https://doi.org/10.4995/agt.2020.13836

Keywords:

irresolvable, disjointly tight, empty interior tightness

Abstract

In this short note we prove the existence (in ZFC) of a completely regular countable disjointly tight irresolvable space by showing that every sub-maximal countable dense subset of 2c is disjointly tight.

Downloads

Download data is not yet available.

Author Biographies

Angelo Bella, University of Catania

Department of Matematics and computer science

Michael Hrusak, Universidad Nacional Autónoma de México

Centro de Ciencias Matemáticas

References

O. T. Alas, M. Sanchis, M. G. Tkacenko, V. V. Tkachuk and R. G. Wilson, Irresolvable and submaximal spaces: Homogeneity versus $sigma$-discreteness and new ZFC examples, Topol. Appl. 107 (2000), 259-273. https://doi.org/10.1016/S0166-8641(99)00111-X

A. Bella and V. I. Malykhin, Tightness and resolvability, Comment. Math. Univ. Carolinae 39, no. 1 (1998), 177-184.

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

R. Engelking, General topology, Heldermann Verlag, Berlin, 1989.

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

I. Juhász, L. Soukup and Z. Szentmiklóssy, D-forced spaces: A new approach to resolvability, Topol. Appl. 153, no. 11 (2006), 1800-1824. https://doi.org/10.1016/j.topol.2005.06.007

K. Kunen, Set theory an introduction to independence proofs, North-Holland, Amsterdam, 1980.