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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Format: | Article |
Language: | English |
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Wiley
1991-01-01
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Series: | International Journal of Mathematics and Mathematical Sciences |
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Online Access: | http://dx.doi.org/10.1155/S0161171291000455 |
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_version_ | 1832566184718893056 |
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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. |
format | Article |
id | doaj-art-27236ad5968d43a085d71caef40d84b2 |
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 |