Vol. 68, No. 2, 1977

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S-spaces in countably compact spaces using Ostaszewski’s method

John Norman Ginsburg

Vol. 68 (1977), No. 2, 393–397
Abstract

A method adapted from that used by A. J. Ostaszewski is used to construct S-spaces as subspaces of given spaces. Assuming the set-theoretic principle , it is shown that every countably compact space containing no nontrivial convergent sequences contains a perfect S-space. As a corollary, assuming , if X is a countably compact F-space, then X contains a hereditarily extremally disconnected, hereditarily normal, perfect S-space.

Mathematical Subject Classification 2000
Primary: 54G05
Milestones
Received: 29 November 1976
Revised: 19 January 1977
Published: 1 February 1977
Authors
John Norman Ginsburg