ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X) | ||
| Journal of Algebraic Systems | ||
| دوره 9، شماره 2، فروردین 2022، صفحه 335-345 اصل مقاله (164.6 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.10325.1510 | ||
| نویسنده | ||
| A. Veisi* | ||
| Faculty of Petroleum and Gas, Yasouj University, Gachsaran, Iran. | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Functionally countable subalgebra؛ m_c-topology؛ pseudocompact space؛ zero-dimensional space | ||
| مراجع | ||
|
1. A. R. Aliabad and R. Mohamadian, On SZ◦-ideals in polynomial rings, Comm. Algebra, 39(2) (2011), 701–717.
2. M. Elyasi, A. A. Estaji and M. Robat Sarpoushi, Locally functionally countable subalgebra of R(L), Arch. Math. (BRNO), 56 (2020), 127–140. 3. R. Engelking, General Topology, Heldermann Verlag Berlin, (1989). 4. A. A. Estaji, A. Karimi Feizabadi and M. Zarghani, Zero elements and z-ideals in modified pointfree topology, Bull. Iran. Math. Soc., 43(7) (2017), 2205–2226. 5. N. J. Fine, L. Gillman and J. Lambek, Rings of quotients of rings of functions, Lecture Notes Series Mc-Gill University Press, Montreal, (1965). 6. M. Ghadermazi, O. A. S. Karamzadeh and M. Namdari, On the functionally countable subalgebra of C(X), Rend. Sem. Mat. Univ. Padova, 129 (2013), 47–69. 7. —————–, C(X) versus its functionally countable subalgebra, Bull. Iran. Math. Soc., 45(1) (2019), 173–187. 8. L. Gillman and M. Jerison, Rings of Continuous Functions, Springer-Verlag, (1976). 9. E. Hewitt, Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc., 64 (1948), 45–99. 10. O. A. S. Karamzadeh and Z. Keshtkar, On c-realcompact spaces, Quaest. Math., 42(8) (2018), 1135–1167. 11. O. A. S. Karamzadeh, M. Namdari and S. Soltanpour, On the locally functionally countable subalgebra of C(X), Appl. Gen. Topol., 16(2) (2015), 183–207. 12. G. D. Maio, L. Hola, D. Holy and R. A. McCoy, Topologies on the space of continuous functions, Topology Appl., 86 (1998), 105–122. 13. M. A. Mulero, Algebraic properties of rings of continuous functions, Fund. Math., 149 (1996), 55–66. 14. M. Namdari and A. Veisi, Rings of quotients of the subalgebra of C(X) consisting of functions with countable image, Int. Math. Forum, 7 (2012), 561–571. 15. A. Veisi, The subalgebras of the functionally countable subalgebra of C(X), Far East J. Math. Sci. (FJMS), 101(10) (2017), 2285–2297. 16. A. Veisi, Invariant norms on the subalgebras of C(X) consisting of bounded functions with countable image, JP Journal of Geometry and Topology, 21(3) (2018), 167–179. 17. A. Veisi, ec-Filters and ec-ideals in the functionally countable subalgebra of C(X), Appl. Gen. Topol., 20(2) (2019), 395–405. | ||
|
آمار تعداد مشاهده مقاله: 551 تعداد دریافت فایل اصل مقاله: 320 |
||