Locally realcompact and HN-complete spaces

David Buhagiar; Emmanuel Chetcuti

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 1, page 107-117
  • ISSN: 0010-2628

Abstract

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Two classes of spaces are studied, namely locally realcompact spaces and HN-complete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non empty support. It is known that a space is locally realcompact if and only if it is open in its Hewitt-Nachbin realcompactification; we give an external characterization of HN-completeness with respect to the Hewitt-Nachbin realcompactification. In addition, a complete characterization of products of these classes is given.

How to cite

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Buhagiar, David, and Chetcuti, Emmanuel. "Locally realcompact and HN-complete spaces." Commentationes Mathematicae Universitatis Carolinae 48.1 (2007): 107-117. <http://eudml.org/doc/250220>.

@article{Buhagiar2007,
abstract = {Two classes of spaces are studied, namely locally realcompact spaces and HN-complete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non empty support. It is known that a space is locally realcompact if and only if it is open in its Hewitt-Nachbin realcompactification; we give an external characterization of HN-completeness with respect to the Hewitt-Nachbin realcompactification. In addition, a complete characterization of products of these classes is given.},
author = {Buhagiar, David, Chetcuti, Emmanuel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Baire measure; realcompactness; local realcompactness; HN-completeness; locally realcompact space; HN-complete space; two-valued Baire measure},
language = {eng},
number = {1},
pages = {107-117},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Locally realcompact and HN-complete spaces},
url = {http://eudml.org/doc/250220},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Buhagiar, David
AU - Chetcuti, Emmanuel
TI - Locally realcompact and HN-complete spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 1
SP - 107
EP - 117
AB - Two classes of spaces are studied, namely locally realcompact spaces and HN-complete spaces, where the latter class is introduced in the paper. Both of these classes are superclasses of the class of realcompact spaces. Invariance with respect to subspaces and products of these spaces are investigated. It is shown that these two classes can be characterized by demanding that certain equivalences hold between certain classes of Baire measures or by demanding that certain classes of Baire measures have non empty support. It is known that a space is locally realcompact if and only if it is open in its Hewitt-Nachbin realcompactification; we give an external characterization of HN-completeness with respect to the Hewitt-Nachbin realcompactification. In addition, a complete characterization of products of these classes is given.
LA - eng
KW - Baire measure; realcompactness; local realcompactness; HN-completeness; locally realcompact space; HN-complete space; two-valued Baire measure
UR - http://eudml.org/doc/250220
ER -

References

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