-closed extensions. II
Authors:
Jack R. Porter and Charles Votaw
Journal:
Trans. Amer. Math. Soc. 202 (1975), 193-209
MSC:
Primary 54D35
DOI:
https://doi.org/10.1090/S0002-9947-1975-0365493-7
MathSciNet review:
0365493
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Abstract | References | Similar Articles | Additional Information
Abstract: The internal structure and external properties (in terms of other -closed extensions) of the Fomin extension
of a Hausdorff space
are investigated. The relationship between
and the Stone-Čech compactification of the absolute of
is developed and used to prove that a
-closed subset of
is compact and to show the existence of a Tychonoff space
such that
is homeomorphic to
. The sequential closure of
in
is shown to be
.
It is known that is not necessarily projectively larger than any other strict
-closed extension of
; a necessary and sufficient condition is developed to determine when a
-closed extension of
is projectively smaller then
. A theorem by Magill is extended by showing that the sets of
-isomorphism classes of
-closed extensions of locally
-closed spaces
and
are lattice isomorphic if and only if
and
are homeomorphic. Harris has characterized those simple Hausdorff extensions of
which are subextensions of the Katětov extension. Characterizations of Hausdorff (not necessarily simple) extensions of
which are subextensions of
-closed extensions
-isomorphic and
-equivalent to the Katětov extension are presented.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1975-0365493-7
Keywords:
-closed extension,
Katětov extension,
Fomin extension,
absolute,
projective cover
Article copyright:
© Copyright 1975
American Mathematical Society