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Heredity of t-pseudocompactness
by
Jerry E. Vaughan
UNC-Greensboro
Let t be an infinite cardinal number. A Tychonoff space X is called t-pseudocompact provided for every continuous f:X® Rt, f(X) is closed in Rt (J. F. Kennison, 1962). Several examples show that t-pseudocompactness is not hereditary to various kinds of closed sets. For instance, Kennison show that t-pseudocompactness is not hereditary to closed C-embedded sets, and H. Ohta (extending examples of T. Retta) showed that t-pseudocompactness is not hereditary to regular-closed sets for t > w (of course, w-pseudocompactness is hereditary to regular-closed sets since w-pseudocompactness is the same as pseudocompactness). S. García-Ferreira and H. Ohta gave a construction intended to produce a t-pseudocompact space X which has a regular-closed zero set B and a regular-closed C-embedded set C such that both B and C are not t-pseudocompact. We noticed, however, that B and C are not regular-closed in X. We show that the construction of García-Ferreira and Ohta produces the desired example by simply replacing the ordinals t+ and w1 in their construction with their long line counterparts.
Date received: March 1, 2005
Copyright © 2005 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # capc-90.