Geodesic
On almost discrete space
Archivum mathematicum, Tome 44 (2008) no. 1, pp. 69-76 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $C(X)$ be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of $C(X)$. The intersection of essential weak ideal in $C(X)$ is also studied.
Let $C(X)$ be the ring of real continuous functions on a completely regular Hausdorff space. In this paper an almost discrete space is determined by the algebraic structure of $C(X)$. The intersection of essential weak ideal in $C(X)$ is also studied.
Classification : 13A30, 54C40
Keywords: essential weak ideal; weak socle; minimal ideal; almost discrete space; scattered space; Stone-Čech compactification; realcompactification 
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a7/}
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Estaji, Ali Akbar. On almost discrete space. Archivum mathematicum, Tome 44 (2008) no. 1, pp. 69-76. http://geodesic.mathdoc.fr/item/ARM_2008_44_1_a7/

[1] Azarpanah, F.: Essential ideals in $C(X)$. Period. Math. Hungar. 3 (12) (1995), 105–112. | DOI | MR | Zbl

[2] Azarpanah, F.: Intersection of essential ideals in $C(X)$. Proc. Amer. Math. Soc. 125 (7) (1997), 2149–2154. | DOI | MR | Zbl

[3] Dietrich, W.: On the ideals in $C(X)$. Trans. Amer. Math. Soc. 152 (1970), 61–77. | DOI | MR

[4] Gillman, L., Jerison, M.: Rings of continuous functions. Springer-Verlag, 1979. | MR

[5] Goodearl, K. R.: Von Neumann regular rings. Pitman, San Francisco, 1979. | MR | Zbl

[6] Henriksen, M., Wilson, R. G.: Almost discrete SV-space. Topology Appl. 46 (1992), 89–99. | DOI | MR | Zbl

[7] Karamzadeh, O. A. S., Rostami, M.: On the intrinsic topology and some related ideals of $C(X)$. Proc. Amer. Math. Soc. 93 (1985), 179–184. | MR | Zbl

[8] Zand, M. R. Ahmadi: Strongly Blumberg space. 5th Annual Iranian Math. Conf. January 26–29, Ahvaz, Iran, 2005.

[9] Zand, M. R. Ahmadi: Strongly Blumberg space. Ph.D. thesis, Shahid Chamran University of Ahvaz in Iran, 2006.