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Title

ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X)

مجله ساختارهای جبری، دوره: 9، شماره: 2
Year: 1401
COI: JR_JAS-9-2_012
Language: EnglishView: 69
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Authors

A. Veisi - Faculty of Petroleum and Gas, Yasouj University, Gachsaran, Iran.

Abstract:

In this paper, we consider the m_c-topology on C_c(X), the functionally countable subalgebra of C(X). We show that a Tychonoff space X is countably pseudocompact if and only if the m_c-topology and the u_c-topology on C_c(X) coincide. It is shown that whenever X is a zero-dimensional space, then C_c(X) is first countable if and only if C(X) with the m-topology is first countable. Also, the set of all zero-divisors of C_c(X) is closed if and only if X is an almost P-space. We show that if X is a strongly zero-dimensional space and U is the set of all units of C_c(X), then the maximal ring of quotients of C_c(U) and C_c(C_c(X)) are isomorphic.

Keywords:

Paper COI Code

This Paper COI Code is JR_JAS-9-2_012. Also You can use the following address to link to this article. This link is permanent and is used as an article registration confirmation in the Civilica reference:

https://civilica.com/doc/1282219/

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Veisi, A.,1401,ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X),https://civilica.com/doc/1282219

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  • M. Elyasi, A. A. Estaji and M. Robat Sarpoushi, Locally ...
  • R. Engelking, General Topology, Heldermann Verlag Berlin, (۱۹۸۹) ...
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  • —————–, C(X) versus its functionally countable subalgebra, Bull. Iran. Math. ...
  • L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, ...
  • E. Hewitt, Rings of real-valued continuous functions, I, Trans. Amer. ...
  • O. A. S. Karamzadeh and Z. Keshtkar, On c-realcompact spaces, ...
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  • G. D. Maio, L. Hola, D. Holy and R. A. ...
  • M. A. Mulero, Algebraic properties of rings of continuous functions, ...
  • M. Namdari and A. Veisi, Rings of quotients of the ...
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Type of center: دانشگاه دولتی
Paper count: 3,424
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