A disjointly tight irresolvable space

Angelo Bella

Italy

University of Catania

Department of Matematics and computer science

Michael Hrusak

Mexico

Universidad Nacional Autónoma de México

Centro de Ciencias Matemáticas

Submitted: 2020-06-11

|

Accepted: 2020-08-25

|

Published: 2020-10-01

DOI: https://doi.org/10.4995/agt.2020.13836
Funding Data

Downloads

Keywords:

irresolvable, disjointly tight, empty interior tightness

Supporting agencies:

This research was not funded

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.

Show more Show less

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.

Show more Show less