Topological Extensions and Subspaces of ηα-sets

Authors

Paul Bankston, Marquette UniversityFollow

Document Type

Article

Language

eng

Format of Original

9 p.

Publication Date

1983

Publisher

Polish Academy of Sciences, Institute of Mathematics

Source Publication

Fundamenta Mathematicae

Source ISSN

0016-2736

Abstract

The η_x-sets of Hausdorff have large compactifications (of cardinality ≽ exp(α); and of cardinality ≽ exp(exp(2^<α)) in the Stone-Čech case). If Q_α denotes the unique (when it exists) η_α -set of cardinality α, then Q_α can be decomposed (= partitioned) into homeomorphs of any prescribed nonempty subspace; moreover the subspaces of Q_α can be characterized as those which arc regular T₁, of cardinality and weight ≼ α, whose topologies are closed under < α intersections.

Comments

Published version. Fundamenta Mathematicae, Vol. 118, No. 3 (1983): 191-199. Publisher Link.© 1983 Polish Academy of Sciences, Institute of Mathematics. Used with permission.

Recommended Citation

Bankston, Paul, "Topological Extensions and Subspaces of ηα-sets" (1983). Mathematics, Statistics and Computer Science Faculty Research and Publications. 201.
https://epublications.marquette.edu/mscs_fac/201