Topology

Polytopological space

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. (Wikipedia).

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Related pages

Bitopological space | Topological space | Kuratowski's closure-complement problem | Monotonic function | Total order | Model theory | General topology | Operator (mathematics) | Closure (topology) | Set (mathematics) | N-topological space | Index set | Partially ordered set | Family of sets | Japaridze's polymodal logic | Ordinal number | Subset