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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