Geodesic
On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 251-260 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

For a Tychonoff space $X$, we obtain a criterion of the $\sigma$-countable compactness of the space of continuous real-valued functions $C(X)$ with the set-open topology. In particular, for extremally disconnected space $X$, we prove that the space $C_\lambda(X)$ is a $\sigma$-countably compact space if and only if $X$ is a pseudocompact space, the set $X(P)$ of all $P$-points of $X$ is dense in $X$, and the family $\lambda$ consists of finite subsets of $X(P)$.
Keywords: set-open topology, $\sigma$-countably compact space, extremally disconnected space, $P$-point, space of continuous functions. 
@article{TIMM_2013_19_3_a25,
     author = {A. V. Osipov and E. G. Pytkeev},
     title = {On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {251--260},
     year = {2013},
     volume = {19},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a25/}
}
TY  - JOUR
AU  - A. V. Osipov
AU  - E. G. Pytkeev
TI  - On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2013
SP  - 251
EP  - 260
VL  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a25/
LA  - ru
ID  - TIMM_2013_19_3_a25
ER  - 
%0 Journal Article
%A A. V. Osipov
%A E. G. Pytkeev
%T On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology
%J Trudy Instituta matematiki i mehaniki
%D 2013
%P 251-260
%V 19
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a25/
%G ru
%F TIMM_2013_19_3_a25
A. V. Osipov; E. G. Pytkeev. On the $\sigma$-countable compactness of spaces of continuous functions with the set-open topology. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 3, pp. 251-260. http://geodesic.mathdoc.fr/item/TIMM_2013_19_3_a25/

[1] Arkhangelskii A. V., Topologicheskie prostranstva funktsii, Mir, M., 1986, 224 pp. | MR

[2] Velichko N. V., “O slaboi topologii prostranstv nepreryvnykh funktsii”, Mat. zametki, 30:5 (1981), 703–712 | MR | Zbl

[3] Gillman L., Jerison M., Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, 1960, 300 pp. | MR | Zbl

[4] Nokhrin S. E., “Some properties of set-open topologies”, J. Math. Sci., 144:3 (2007), 4123–4151 | DOI | MR | Zbl

[5] Osipov A. V., “Topological-algebraic properties of function spaces with set-open topologies”, Topology Appl., 159:3 (2012), 800–805 | DOI | MR | Zbl

[6] Tkačuk V. V., “The spaces $C_p(X)$: decomposition into a countable union of bounded subspaces and completeness properties”, Topology Appl., 22:3 (1986), 241–253 | DOI | MR | Zbl