Measure characterizations and properties of normal and regular lattices

Various equivalent characterizations of normality are considered and a measure theoretic definition is given for strongly normal lattices. Measure conditions related to the apace of σ-smooth, lattice-regular, 0−1 measures are noted which imply, or are equivalent to, the space being Hausdorff, regula...

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Main Author: Peter M. Grassi
Format: Article
Language:English
Published: Wiley 1991-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171291000455
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author Peter M. Grassi
author_facet Peter M. Grassi
author_sort Peter M. Grassi
collection DOAJ
description Various equivalent characterizations of normality are considered and a measure theoretic definition is given for strongly normal lattices. Measure conditions related to the apace of σ-smooth, lattice-regular, 0−1 measures are noted which imply, or are equivalent to, the space being Hausdorff, regular, or prime complete.
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institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 1991-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-27236ad5968d43a085d71caef40d84b22025-02-03T01:04:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251991-01-0114238539210.1155/S0161171291000455Measure characterizations and properties of normal and regular latticesPeter M. Grassi0Department of Mathematics, Hofstra University, Hempstead 11550, New York, USAVarious equivalent characterizations of normality are considered and a measure theoretic definition is given for strongly normal lattices. Measure conditions related to the apace of σ-smooth, lattice-regular, 0−1 measures are noted which imply, or are equivalent to, the space being Hausdorff, regular, or prime complete.http://dx.doi.org/10.1155/S0161171291000455latticezero-one measuressigma-smoothnormalregular Hausdorffprime completestrongly normalfilterdisjunctive.
spellingShingle Peter M. Grassi
Measure characterizations and properties of normal and regular lattices
International Journal of Mathematics and Mathematical Sciences
lattice
zero-one measures
sigma-smooth
normal
regular
Hausdorff
prime complete
strongly normal
filter
disjunctive.
title Measure characterizations and properties of normal and regular lattices
title_full Measure characterizations and properties of normal and regular lattices
title_fullStr Measure characterizations and properties of normal and regular lattices
title_full_unstemmed Measure characterizations and properties of normal and regular lattices
title_short Measure characterizations and properties of normal and regular lattices
title_sort measure characterizations and properties of normal and regular lattices
topic lattice
zero-one measures
sigma-smooth
normal
regular
Hausdorff
prime complete
strongly normal
filter
disjunctive.
url http://dx.doi.org/10.1155/S0161171291000455
work_keys_str_mv AT petermgrassi measurecharacterizationsandpropertiesofnormalandregularlattices