Variants of openness |
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Authors: | B Banaschewski A Pultr |
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Institution: | (1) Department of Mathematics and Statistics, McMaster University, L8S 4K1 Hamilton, Ontario, Canada;(2) Department of Applied Mathematics, Charles University, Prague, Czech Republic |
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Abstract: | Algebraic conditions on frame homomorphisms representing various types of openness requirements on continuous maps are investigated. It turns out that several of these can be expressed in terms of formulas involving pseudocomplements. A full classification of the latter is presented which shows that they group into five equivalence classes and establishes the logical connections between them. Among the relation of our algebraic conditions to continuous maps between topological spaces, we establish that the coincidence of the algebraic and topological notion of openness is equivalent to the separation axiomT
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for the domain space.In honour of Dieter Pumplün on the occassion of his 60th birthday |
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Keywords: | 06D10 06D99 54C10 54D10 |
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