TY - JOUR
AU - Tarizadeh, Abolfazl
PY - 2013/07/02
Y2 - 2023/12/02
TI - On the category of profinite spaces as a reflective subcategory
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 14
IS - 2
SE -
DO - 10.4995/agt.2013.1575
UR - https://ojs.upv.es/index.php/AGT/article/view/1575
SP - 147-157
AB - 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 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 $X$.
ER -