Geodesic
On the completeness properties of the $C$-compact-open topology on $C(X)$
Ural mathematical journal, Tome 1 (2015) no. 1, pp. 61-67 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This is a study of the completeness properties of the space $C_{rc}(X)$ of continuous real-valued functions on a Tychonoff space $X$, where the function space has the $C$-compact-open topology. Investigate the properties such as completely metrizable, Čech-complete, pseudocomplete and almost Čech-complete.
Keywords: $C$-compact-open topology, Set-open topology, Čech-complete, Function space.
Mots-clés : Baire space 
@article{UMJ_2015_1_1_a5,
     author = {Alexander V. Osipov},
     title = {On the completeness properties of the $C$-compact-open topology on $C(X)$},
     journal = {Ural mathematical journal},
     pages = {61--67},
     year = {2015},
     volume = {1},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a5/}
}
TY  - JOUR
AU  - Alexander V. Osipov
TI  - On the completeness properties of the $C$-compact-open topology on $C(X)$
JO  - Ural mathematical journal
PY  - 2015
SP  - 61
EP  - 67
VL  - 1
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a5/
LA  - en
ID  - UMJ_2015_1_1_a5
ER  - 
%0 Journal Article
%A Alexander V. Osipov
%T On the completeness properties of the $C$-compact-open topology on $C(X)$
%J Ural mathematical journal
%D 2015
%P 61-67
%V 1
%N 1
%U http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a5/
%G en
%F UMJ_2015_1_1_a5
Alexander V. Osipov. On the completeness properties of the $C$-compact-open topology on $C(X)$. Ural mathematical journal, Tome 1 (2015) no. 1, pp. 61-67. http://geodesic.mathdoc.fr/item/UMJ_2015_1_1_a5/

[1] Nokhrin S.E., Osipov A.V., “On the coincidence of the set-open and uniform topologies”, Proc. Steklov Inst. Math. (Suppl.), 267:1, suppl. (2009), S184–S191 | DOI

[2] Osipov A.V., “Weakly set-open topology”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 2, 2010, 167–176 (in Russian)

[3] Osipov A.V., “Properties of the $C$-compact-open topology on a function space”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 258–277 (in Russian)

[4] Osipov A.V., Kosolobov D.A., “On sequentially compact-open topology”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2011, no. 3, 75–84 (in Russian)

[5] Engelking R, General Topology, PWN, Warsaw, 1977, 752 pp.

[6] Aarts J.M., Lutzer D.J., “Pseudo-completeness and the product of Baire spaces”, Pacific. J. Math., 1973, no. 48, 1–10

[7] Arens R., Dugundji J., “Topologies for function spaces”, Pacific J. Math., 1:1 (1951), 5–31

[8] Arhangel’skii A.V., Tkachenko M., Topological group and related structures., Atlantis Stud. Math., 1, Atlantis Press,, Paris, 2008, 800 pp.

[9] Aull C.E., “Sequences in topological spaces”, Prace Mat., 11 (1968), 329–336

[10] Buhagiar D., Yoshioka I., “Sieves and completeness properties”, Questions Answers Gen. Topology, 2000, no. 18, 143–162

[11] Frolik Z., “Generalizations of the $G_{\delta}$-property of complete metric spaces”, Czech. Math. J, 10:3 (1960), 359–379

[12] Gillman L., Jerison M., Rings of continuous functions, The University Series in Higher Mathematics., D. Van Nostrand Co., Inc., Princeton, New Jersey, 1960, 300 pp.

[13] Kundu S., Garg P., “The pseudocompact-open topology on $C(X)$”, Topology Proceedings, 30 (2006), 279–299

[14] Kundu S., Raha A.B., “The bounded-open topology and its relatives”, Rend. Istit. Mat. Univ. Trieste, 27 (1995), 61–77

[15] Kundu S., Garg P., “Completeness properties of the pseudocompact-open topology on $C(X)$”, Math. Slovaca, 58:3 (2008), 325–338

[16] Michael E., “Almost complete spaces, hypercomplete spaces and related mapping theorems”, Topology Appl., 1991, no. 41, 113–130

[17] Michael E., “Partition-complete spaces are preserved by tri-quotient maps”, Topology Appl., 1992, no. 44, 235–240

[18] Osipov A.V., “The Set-Open topology”, Top. Proc., 2011, no. 37, 205–217

[19] Osipov A.V., “Topological-algebraic properties of function spaces with set-open topologies”, Topology and its Applications, 159:3 (2012), 800–805

[20] Oxtoby J.C., “Cartesian products of Baire spaces”, Fund. Math., 1961, no. 49, 157–166

[21] Taylor A.E., Lay D.C., Introduction to functional analysis, 2nd ed., John Wiley Sons, New York, 1980, 244 pp.