About: Polytopological space

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In general topology, a polytopological space consists of a set together with a family of topologies on that is linearly ordered by the inclusion relation ( is an arbitrary index set). It is usually assumed that the topologies are in non-decreasing order, but some authors prefer to put the associated closure operators in non-decreasing order (operators and satisfy if and only if for all ), in which case the topologies have to be non-increasing.

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  • In general topology, a polytopological space consists of a set together with a family of topologies on that is linearly ordered by the inclusion relation ( is an arbitrary index set). It is usually assumed that the topologies are in non-decreasing order, but some authors prefer to put the associated closure operators in non-decreasing order (operators and satisfy if and only if for all ), in which case the topologies have to be non-increasing. Polytopological spaces were introduced in 2008 by the philosopher for the purpose of defining a topological model of Japaridze's polymodal logic (GLP). They subsequently became an object of study in their own right, specifically in connection with Kuratowski's closure-complement problem. (en)
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  • In general topology, a polytopological space consists of a set together with a family of topologies on that is linearly ordered by the inclusion relation ( is an arbitrary index set). It is usually assumed that the topologies are in non-decreasing order, but some authors prefer to put the associated closure operators in non-decreasing order (operators and satisfy if and only if for all ), in which case the topologies have to be non-increasing. (en)
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  • Polytopological space (en)
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