Geodesic
Intersections of minimal prime ideals in the rings of continuous functions
Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 623-632

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

A space $X$ is called $\mu $-compact by M. Mandelker if the intersection of all free maximal ideals of $C(X)$ coincides with the ring $C_K(X)$ of all functions in $C(X)$ with compact support. In this paper we introduce $\phi $-compact and $\phi '$-compact spaces and we show that a space is $\mu $-compact if and only if it is both $\phi $-compact and $\phi '$-compact. We also establish that every space $X$ admits a $\phi $-compactification and a $\phi '$-compactification. Examples and counterexamples are given.
Classification : 46E25, 46J20, 54C40
Keywords: minimal prime ideal; $P$-space; $F$-space; $\mu$-compact space; $\phi $-compact space; $\phi '$-compact space; round subset; almost round subset; nearly round subset 
@article{CMUC_2006__47_4_a7,
     author = {Ghosh, Swapan Kumar},
     title = {Intersections of minimal prime ideals in the rings of continuous functions},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {623--632},
     publisher = {mathdoc},
     volume = {47},
     number = {4},
     year = {2006},
     mrnumber = {2337417},
     zbl = {1150.54018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a7/}
}
TY  - JOUR
AU  - Ghosh, Swapan Kumar
TI  - Intersections of minimal prime ideals in the rings of continuous functions
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 2006
SP  - 623
EP  - 632
VL  - 47
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a7/
LA  - en
ID  - CMUC_2006__47_4_a7
ER  - 
%0 Journal Article
%A Ghosh, Swapan Kumar
%T Intersections of minimal prime ideals in the rings of continuous functions
%J Commentationes Mathematicae Universitatis Carolinae
%D 2006
%P 623-632
%V 47
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a7/
%G en
%F CMUC_2006__47_4_a7
Ghosh, Swapan Kumar. Intersections of minimal prime ideals in the rings of continuous functions. Commentationes Mathematicae Universitatis Carolinae, Tome 47 (2006) no. 4, pp. 623-632. http://geodesic.mathdoc.fr/item/CMUC_2006__47_4_a7/