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Zbl 0837.54012
Watson, Stephen; Wilson, Richard G.
Embeddings in connected spaces. (English)
[J] Houston J. Math. 19, No.3, 469-481 (1993). ISSN 0362-1588

Summary: We obtain some sufficient conditions for a Hausdorff space $X$ to be embeddable as a dense subset of a connected Hausdorff space. Some examples are given to show that, in the general case, these conditions are not necessary, while in the case that $X$ is countable, necessary and sufficient conditions are given. Some other types of embeddings are also considered.

MSC 2000:: *54D05 Connectedness (general aspects)
54C25 Imbedding of topological spaces
54D25 "P-minimal" and "P-closed" spaces

Keywords: connectification; $H$-closed subspace; feebly compact space; free open ultrafilter; $\sigma$-discrete $\pi$-base; countable $\pi$-base

Cited in: Zbl 0928.54018 Zbl 0928.54017 Zbl 0887.54018 Zbl 0914.54020 Zbl 0855.54026 Zbl 0855.54025

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