Geodesic
A class of free locally convex spaces
Sbornik. Mathematics, Tome 194 (2003) no. 3, pp. 333-360 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Stratifiable spaces are a natural generalization of metrizable spaces for which Dugundji's theorem holds. It is proved that the free locally convex space of a stratifiable space is stratifiable. This means, in particular, that the space of finitely supported probability measures on a stratifiable space is a retract of a locally convex space, and that each stratifiable convex subset of a locally convex space is a retract of a locally convex space. 
@article{SM_2003_194_3_a1,
     author = {O. V. Sipacheva},
     title = {A class of free locally convex spaces},
     journal = {Sbornik. Mathematics},
     pages = {333--360},
     year = {2003},
     volume = {194},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_3_a1/}
}
TY  - JOUR
AU  - O. V. Sipacheva
TI  - A class of free locally convex spaces
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 333
EP  - 360
VL  - 194
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_3_a1/
LA  - en
ID  - SM_2003_194_3_a1
ER  - 
%0 Journal Article
%A O. V. Sipacheva
%T A class of free locally convex spaces
%J Sbornik. Mathematics
%D 2003
%P 333-360
%V 194
%N 3
%U http://geodesic.mathdoc.fr/item/SM_2003_194_3_a1/
%G en
%F SM_2003_194_3_a1
O. V. Sipacheva. A class of free locally convex spaces. Sbornik. Mathematics, Tome 194 (2003) no. 3, pp. 333-360. http://geodesic.mathdoc.fr/item/SM_2003_194_3_a1/

[1] Dugundji J., “An extension of Tietze's theorem”, Pacific J. Math., 1 (1951), 353–367 | MR | Zbl

[2] Borges C. J. R., “On stratifiable spaces”, Pacific J. Math., 17:1 (1966), 1–16 | MR | Zbl

[3] Gruenhage G., “Generalized metric spaces”, Handbook of Set-Theoretic Topology, eds. K. Kunen, J. E. Vaughan, North-Holland, Amsterdam, 1984, 423–501 | MR

[4] Uspenskii V. V., “Svobodnye topologicheskie gruppy metrizuemykh prostranstv”, Izv. AN SSSR. Ser. matem., 54:6 (1990), 1295–1319 | MR | Zbl

[5] Fedorchuk V. V., “The Suslin number of the functor of probability measures”, Topology Appl., 84 (1998), 55–60 | DOI | MR | Zbl

[6] Tkachenko M. G., “O svoistve Suslina v svobodnykh topologicheskikh gruppakh nad bikompaktami”, Matem. zametki, 34:4 (1983), 601–607 | MR | Zbl

[7] Stone A. H., “On the compactification of topological spaces”, Ann. Soc. Polon. Math., 21 (1948), 153–160 | MR | Zbl

[8] Engelking R., Obschaya topologiya, Mir, M., 1986 | MR

[9] Raikov D. A., “Svobodnye lokalno vypuklye prostranstva ravnomernykh prostranstv”, Matem. sb., 63:4 (1964), 582–590 | MR | Zbl

[10] Przymusiński T., “Collectionwise normality and extensions of continuous functions”, Fund. Math., 98:1 (1978), 75–81 | MR | Zbl

[11] Tukey J. W., Convergence and uniformity in topology, Princeton Univ. Press, Princeton, NJ, 1940 | MR | Zbl

[12] Heath R. W., Hodel R. E., “Characterizations of $\sigma$-spaces”, Fund. Math., 77:3 (1973), 271–275 | MR | Zbl