Local Connectedness Of Extension Spaces

Bernhard Banaschewski

doi:10.4153/CJM-1956-044-8

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1. Introduction. An extension E* of a topological space E (that is, a space containing E as a dense subspace) determines a family of filters (u) on E, given by the traces U ∩ E of the neighbourhoods U ⊆ E* of each u ∈ E* − E. Many topological properties of an extension E* of a given space E can be related to properties of these trace filters (as we shall call them) belonging to E*.

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