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- W2950897464 abstract "In this paper by using the ring of real-valued continuous functions $C(X)$, we prove a theorem in profinite spaces which states that for a compact Hausdorff space $X$, the set of its connected components $X/_{sim}$ endowed with some topology $mathscr{T}$ is a profinite space. Then we apply this result to give an alternative proof to the fact that the category of profinite spaces is a reflective subcategory in the category of compact Hausdorff spaces. Finally, under some circumstances on a space $X$, we compute the connected components of the space $t(X)$ in terms of the ones of the space $X$." @default.
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- W2950897464 date "2012-07-25" @default.
- W2950897464 modified "2023-09-27" @default.
- W2950897464 title "On the category of profinite spaces as a reflective subcategory" @default.
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