Some generalizations of the Stone Duality Theorem (Q2915398)
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scientific article; zbMATH DE number 6083231
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some generalizations of the Stone Duality Theorem |
scientific article; zbMATH DE number 6083231 |
Statements
Some generalizations of the Stone Duality Theorem (English)
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17 September 2012
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duality
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contravariant adjunction
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local Boolean algebra
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ZLB-algebra
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generalized Boolean algebra
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locally compact (compact) zero-dimensional space
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skeletal map
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perfect map
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(quasi-)open map
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(dense) embedding
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injective (surjective) map
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Let BoolSp be the category of zero-dimensional locally compact Hausdorff spaces and continuous mappings. The paper studies modifications of Stone duality. Several modifications of Boolean algebra that form dual categories of BoolSp are presented. The dual categories of subcategories of BoolSp formed by selection of special morphisms (all perfect maps, all open perfect maps, all skeletal maps, all quasi-open perfect maps, all open maps) are given. The characterizations of the dual maps of injective or surjective maps of BoolSp are presented. These results are generalized on subcategories of BoolSp created by compact spaces.
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