On the category of profinite spaces as a reflective subcategory

Applied General Topology

Abolfazl Tarizadeh¹ 

[1] University of Maragheh;

关键词: profinite spaces;    connected components;    coarser topology;    reflective subcategory;   

DOI  :  10.4995/agt.2013.1575

来源: DOAJ

【 摘 要 】

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 the quotient topology 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 compactHausdorff 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 $X$.

【 授权许可】

Unknown