5:43 AM
I thought that, in order to be consistent, if we have tag for compactness then connectedness could be equally important. (And connectedness seemed to me better name than connected-sets.)
I even prepared some rough draft of tag-excerpt: Use this tag for question on connected spaces and various related notions (connected components, locally connected spaces, path-connected spaces, arcwise connected spaces,totally disconnected spaces,...)
And tag-wiki: A topological space is [connected](http://en.wikipedia.org/wiki/Connected_space) if it cannot be written as union of two disjoint non-empty open sets.
Every topological space can be partition into connected components.
Every topological space can be partition into connected components.
* [locally connected spaces](http://en.wikipedia.org/wiki/Locally_connected_space)
* path-connected spaces
* arcwise connected spaces
* [totally disconnected spaces](http://en.wikipedia.org/wiki/Totally_disconnected_space)
* path-connected spaces
* arcwise connected spaces
* [totally disconnected spaces](http://en.wikipedia.org/wiki/Totally_disconnected_space)
Today connectedness appeared among new tags; it was created in this question, which is about connectedness in graph theory.
So the question is: Do we want connectedness? Should it be only for the meaning of this word in general topology, of for other meanings too? (Apart from topology and graph theory, Wikipedia mentions connected categories. Although I don't think there will be many questions about them.)
6:16 AM
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