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Embeddings in connected spaces. (English) Zbl 0837.54012
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:
54D05 Connected and locally connected spaces (general aspects)
54C25 Embedding
54D25 “\(P\)-minimal” and “\(P\)-closed” spaces
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