On the category of profinite spaces as a reflective subcategory

Authors

  • Abolfazl Tarizadeh University of Maragheh

DOI:

https://doi.org/10.4995/agt.2013.1575

Keywords:

profinite spaces, connected components, coarser topology, reflective subcategory

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 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 $X$.

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Author Biography

Abolfazl Tarizadeh, University of Maragheh

Faculty of Basic Sciences

References

R. Bkouche, Couples spectraux et faisceaux associés. Applications aux anneaux de fonctions, Bull. Soc. Math. France 98 (1970), 253-295.

F. Borceux and G. Janelidze, Galois Theories, Cambridge University Press, 2001. http://dx.doi.org/10.1017/CBO9780511619939

T. C. Craven, The Boolean space of orderings of a field}, Trans. Amer. Math. Soc. 209 (1975), 225-235. http://dx.doi.org/10.1090/S0002-9947-1975-0379448-X

L. Gillman and M. Jerison, Rings of Continuous Functions, Springer, 1976.

T. Szamuely, Galois Groups and Fundamental Groups, Cambridge Studies in Adv. Math., vol 117, 2009. http://dx.doi.org/10.1017/CBO9780511627064

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Published

2013-07-02

How to Cite

[1]
A. Tarizadeh, “On the category of profinite spaces as a reflective subcategory”, Appl. Gen. Topol., vol. 14, no. 2, pp. 147–157, Jul. 2013.

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Section

Articles