# Tagged Questions

Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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### If there exist compact dense subset of a topological space, then can we say about the compactiness of topological space? [on hold]

Let (X,T) be a topological space and there is A subset of X and is compact then (X,T) is compact? If not then what be the counter example for this statement?
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### If we find compactification of dense subset of a topological spaces, then what can we say about compactification of original space? [on hold]

Let $(X,T)$ be a topological space and $F$ a dense subset of $X$. Suppose that we have compactification of $(F,T)$, $(f,\beta F)$. Does $(X,T)$ possess a compactification?
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### Topological properties via properties continuous maps

A topological space $(X,\tau)$ is connected if and only if the only continuous maps $f:X\to\{0,1\}$ (where $\{0,1\}$ carries the discrete topology) are the constant maps. Are there other examples of ...
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### Meaning of Regular Neighborhood for Homology Basis Curves in $S_{g,2}$
I have been trying to understand the meaning of the expression "regular neighborhood" in the context described below, but I'm stuck: We have a collection of curves $c_i$ for $i=1,2,..,n$ embedded in ...