A note on homeomorphic realcompactifications

McArthur, William G.

doi:10.1007/bf01222544

Cited by 3 publications

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“…We also consider a number of related questions. We have been strongly motivated by the work of Gillman and Jerison [5] and McArthur [9], where analogous problems for the Stone-Cech compactification and the Hewitt realcompactification have been handled respectively.…”

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confidence: 99%

A Note on H-Closed Extensions of a Product

D'Aristotle

1976

Can. math. bull.

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Any Hausdorff space X is a dense subspace of an H-closed space κX, called the Katětov extension of X, with the property that any H-closed extension Y of X is a continuous image of κX under a mapping which leaves X pointwise fixed [8], [10]. In [8], Liu has shown that the extensions κ(X×Y) and κX×κY of X × Y are equal iff (1) X or Y is finite, or (2) X and Y are H-closed. In this note, we examine whether homeomorphism of these two extensions implies equality. We give a condition under which homeomorphism implies equality and an example to show that this relation does not hold in general.

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confidence: 99%

A Note on H-Closed Extensions of a Product

D'Aristotle

1976

Can. math. bull.

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1975

North-Holland Mathematics Studies

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Realcompactifications of products of ordered spaces

McArthur¹

1973

Proc. Amer. Math. Soc.

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The equality υ ( X × Y ) = υ X × υ Y \upsilon (X \times Y) = \upsilon X \times \upsilon Y is studied for the case when one of the factors is a linearly ordered topological space (LOTS). Among the results obtained are the following: 1. If X X is any separable realcompact space and Y Y is any LOTS of nonmeasurable cardinal, then υ ( X × Y ) = υ X × υ Y \upsilon (X \times Y) = \upsilon X \times \upsilon Y . 2. If X X is a nonparacompact LOTS, then there is a paracompact LOTS Y Y such that υ ( X × Y ) ≠ υ X × υ Y \upsilon (X \times Y) \ne \upsilon X \times \upsilon Y . 3. For any pair X , Y X,Y of well-ordered spaces, υ ( X × Y ) = υ X × υ Y \upsilon (X \times Y) = \upsilon X \times \upsilon Y .

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A note on homeomorphic realcompactifications

Cited by 3 publications

References 4 publications

A Note on H-Closed Extensions of a Product

A Note on H-Closed Extensions of a Product

Bibliography

Realcompactifications of products of ordered spaces

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