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On strict and simple type extensions. (English) Zbl 0895.54012

An extension of a topological space \((X,\tau')\) is a topological space \((Y,\tau)\) that contains \((X,\tau')\) as a dense subspace. In this paper filter systems on \((X,\tau')\) using regular open sets of \((X,\tau')\) are used to construct new topologies on \(Y\), some of which yield nice extensions of \((X,\tau')\). Connections to the strict and simple extensions of \((X,\tau')\) are investigated.

MSC:

54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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