On some questions on selectively highly divergent spaces

Angelo Bella; Santi Spadaro

doi:10.4995/agt.2024.20387

Authors

Angelo Bella University of Catania
Santi Spadaro Università di Palermo https://orcid.org/0000-0001-5880-8799

DOI:

https://doi.org/10.4995/agt.2024.20387

Keywords:

Convergent sequences, Splitting number, Stone-Cech compactification, Selectively highly divergent spaces, Pixley-Roy hyper-space

Abstract

A topological space X is selectively highly divergent (SHD) if for every sequence of non-empty open sets { U_n : n ∈ ω } of X, we can find x_n ∈ U_n such that the sequence {x_n : n ∈ ω } has no convergent subsequences. In this note we answer two questions related to this notion asked by Jiménez-Flores, Ríos-Herrejón, Rojas-Sánchez and Tovar-Acosta.

Downloads

Download data is not yet available.

Author Biographies

Angelo Bella, University of Catania

Dipartimento di Matematica e Informatica

Santi Spadaro, Università di Palermo

Dipartimento di Ingegneria

References

E. K. van Douwen, Applications of maximal topologies, Topology Appl. 51 (1993), 125-140. https://doi.org/10.1016/0166-8641(93)90145-4

E. K. van Douwen, The Integers and Topology, Handbook of Set-theoretic Topology (K. Kunen and J. E. Vaughan Editors), Elsevier Science Publishers B.V., Amsterdam (1984), 111-167. https://doi.org/10.1016/B978-0-444-86580-9.50006-9

R. Engelking, General Topology, Sigma Series in Pure Mathematics 6 Berlin: Heldermann Verlag, 1989.

C. D. Jimenez-Flores, A. Rios-Herrejon, A. D. Rojas-Sanchez and E. E. Tovar-Acosta, On selectively highly divergent spaces, ArXiv:2307.11992.

K. Kunen, Set Theory, Studies in Logic (London) 34. London: College Publications viii, 401 p. (2011).