\(\alpha\)-continuous and \(\alpha\)-open mappings (Q790475)
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scientific article; zbMATH DE number 3848207
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(\alpha\)-continuous and \(\alpha\)-open mappings |
scientific article; zbMATH DE number 3848207 |
Statements
\(\alpha\)-continuous and \(\alpha\)-open mappings (English)
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1983
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A subset S of a topological X is called an \(\alpha\)-set if \(S\subset int(cl(int S))\). A mapping f:\(X\to Y\) is called \(\alpha\)-continuous if the inverse image of each open set in Y is an \(\alpha\)-set in X and \(\alpha\)-open if the image of each open set in X is an \(\alpha\)-set in Y. This paper studies these classes of mappings, and especially their relationships with other classes of mappings.
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\(\alpha\)-set
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semi-open set
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preopen set
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\(\alpha\)-continuity
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\(\alpha\)- open mappings
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