Abstract
If X is a regular hereditary Souslin space and x ∈X then either there exists a sequence {xn: n=1, 2, ...} ⊂ X{x} such that x ∈ [{xn∶n=1, 2, ...}], or the pseudocharacter of x in X is no greater than countable. In other words, if X is a hereditary Souslin bicompactum which is a χ-space, then X is a Frechet-Urysohn space.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature cited
A. V. Arkhangel'skii and V. I. Ponomarev, “On dyadic bicompacta,” Dokl. Akad. Nauk SSSR, 182, No. 5, 993–996 (1968).
A. V. Arkhangel'skii, “Souslin numbers and powers, characteristic points of separable bicompacta,” Dokl. Akad. Nauk SSSR, 192, No. 2, 255–258 (1970).
N. Shanin, “On products of topological spaces,” Tr. Matem. In-ta Akad. Nauk SSSR (1948), Vol. 24.
P. S. Aleksandrov and P. S. Urysohn, “Memoir on compact topological spaces,” Tr. Matem. In-ta Akad. Nauk SSSR (1950), Vol. 31.
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 281–288, February, 1974.
Rights and permissions
About this article
Cite this article
Shapirovskii, B.É. Spaces with a Souslin and a shanin condition. Mathematical Notes of the Academy of Sciences of the USSR 15, 161–164 (1974). https://doi.org/10.1007/BF02102399
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02102399