On the category of profinite spaces as a reflective subcategory
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 t...
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Universitat Politècnica de València
2013-07-01
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| Series: | Applied General Topology |
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| Online Access: | http://polipapers.upv.es/index.php/AGT/article/view/1575 |
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doaj-a89d59dd4a7f40f4a29d66f2658d2c472020-11-24T22:43:43ZengUniversitat Politècnica de ValènciaApplied General Topology1576-94021989-41472013-07-0114214715710.4995/agt.2013.15751299On the category of profinite spaces as a reflective subcategoryAbolfazl Tarizadeh0University of MaraghehIn 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 $X$.http://polipapers.upv.es/index.php/AGT/article/view/1575profinite spacesconnected componentscoarser topologyreflective subcategory |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Abolfazl Tarizadeh |
| spellingShingle |
Abolfazl Tarizadeh On the category of profinite spaces as a reflective subcategory Applied General Topology profinite spaces connected components coarser topology reflective subcategory |
| author_facet |
Abolfazl Tarizadeh |
| author_sort |
Abolfazl Tarizadeh |
| title |
On the category of profinite spaces as a reflective subcategory |
| title_short |
On the category of profinite spaces as a reflective subcategory |
| title_full |
On the category of profinite spaces as a reflective subcategory |
| title_fullStr |
On the category of profinite spaces as a reflective subcategory |
| title_full_unstemmed |
On the category of profinite spaces as a reflective subcategory |
| title_sort |
on the category of profinite spaces as a reflective subcategory |
| publisher |
Universitat Politècnica de València |
| series |
Applied General Topology |
| issn |
1576-9402 1989-4147 |
| publishDate |
2013-07-01 |
| description |
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 $X$. |
| topic |
profinite spaces connected components coarser topology reflective subcategory |
| url |
http://polipapers.upv.es/index.php/AGT/article/view/1575 |
| work_keys_str_mv |
AT abolfazltarizadeh onthecategoryofprofinitespacesasareflectivesubcategory |
| _version_ |
1725694924679020544 |