On iterated de Groot dualizations of topological spaces (Q1763583)
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scientific article; zbMATH DE number 2136456
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On iterated de Groot dualizations of topological spaces |
scientific article; zbMATH DE number 2136456 |
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On iterated de Groot dualizations of topological spaces (English)
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22 February 2005
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In 2001 the author solved an open problem of J. D. Lawson and M. Mislove (Problem 540 in Open Problems in Topology) by showing that the process of taking (de Groot) duals terminates after finitely many steps with topologies that are duals of each other. In the present paper the author proves a new identity for dual topologies, namely that \(\tau^d=(\tau \vee \tau^{dd})^d\) . In addition, a solution to another open problem is also presented.
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saturated set
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dual topology
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compactness operator
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