Embeddings into countably compact Hausdorff spaces

  • Taras Banakh Ivan Franko National University of Lviv and Jan Kochanowski University in Kielce, Poland)
  • Serhii Bardyla Institute of Mathematics, P. J. Šafárik University in Košice, Slovakia
  • Alex Ravsky Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, Lviv


UDC 515.122

We consider the problem of characterization of topological spaces  embedded into countably compact Hausdorff topological spaces. We study the separation axioms for subspaces of Hausdorff countably compact topological spaces and construct an example of a regular separable scattered topological space that cannot be embedded into a Urysohn countably compact topological space.


T. Banakh, On $κ$-bounded and $M$-compact reflections of topological spaces, Topology and Appl., 289, Article 107547 (2021).

T. Banakh, S. Bardyla, A. Ravsky, Embedding topological spaces into Hausdorff $kappa$-bounded spaces, Topology and Appl., 280, Article 107277 (2020).

T. Banakh, J. Mioduszewski, S. Turek, On continuous self-maps and homeomorphisms of the Golomb space, Comment. Math. Univ. Carolin., 59, № 4, 423–442 (2018).

S. Bardyla, Embedding of regular spaces in countably compact Hausdorff spaces, Lviv Scottish Book; https://math-overflow.net/q/339657/61536.

E. K. van Douwen, The integers and topology, Handbook of Set-Theoretic Topology, North-Holland, Amsterdam (1984), p. 111–167.

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

S. García-Ferreira, Lj. Kočinac, Convergence with respect to ultrafilters: a survey, Filomat, № 10, 1–32 (1996).

I. Juhász, J. van Mill, W. Weiss, Variations on $w$-boundedness, Israel J. Math., 194, № 2, 745–766 (2013).

I. Juhász, S. Shelah, L. Soukup, More on countably compact, locally countable spaces, Israel J. Math., 62, № 3, 302–310 (1988).

I. Juhász, J. Vaughan, Countably compact hyperspaces and Frolík sums, Topology and Appl., 154, № 12, 2434–2448 (2007).

P. Nyikos, First countable, countably compact, noncompact spaces, Open Problems in Topology II, Elsevier (2007), p. 217–224.

J. Vaughan, Countably compact and sequentially compact spaces, Handbook of Set-Theoretic Topology, Elsevier (1984), p. 569–602.

How to Cite
Banakh, T., S. Bardyla, and A. Ravsky. “Embeddings into Countably Compact Hausdorff Spaces”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, no. 8, Aug. 2023, pp. 1032 -42, doi:10.3842/umzh.v75i8.2283.
Research articles