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Mat. Sb., 2003, Volume 194, Number 3, Pages 25–52 (Mi msb719)  

This article is cited in 7 scientific papers (total in 7 papers)

A class of free locally convex spaces

O. V. Sipacheva

M. V. Lomonosov Moscow State University

Abstract: 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.

DOI: https://doi.org/10.4213/sm719

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English version:
Sbornik: Mathematics, 2003, 194:3, 333–360

Bibliographic databases:

UDC: 515.12
MSC: Primary 54E20, 46A03; Secondary 54C15
Received: 23.07.2002

Citation: O. V. Sipacheva, “A class of free locally convex spaces”, Mat. Sb., 194:3 (2003), 25–52; Sb. Math., 194:3 (2003), 333–360

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. V. Sipacheva, “The topology of free topological groups”, J. Math. Sci., 131:4 (2005), 5765–5838  mathnet  crossref  mathscinet  zmath  elib  elib
    2. Shkarin S.A., “Monotonically normal topological vector spaces are stratifiable”, Topology Appl., 136:1-3 (2004), 129–134  crossref  mathscinet  zmath  isi  elib
    3. Karassev A., Tuncali M., Valov V, “Finite-to-one maps into Euclidean manifolds and spaces with disjoint disks properties”, Topology and Its Applications, 157:4 (2010), 779–788  crossref  mathscinet  zmath  isi  elib
    4. Banakh T., Valov V., “Approximation by light maps and parametric Lelek maps”, Topology and Its Applications, 157:15 (2010), 2325–2341  crossref  mathscinet  zmath  isi  elib
    5. Banakh T., Valov V., “Spaces with fibered approximation property in dimension n”, Central European Journal of Mathematics, 8:3 (2010), 411–420  crossref  mathscinet  zmath  isi
    6. Banakh T. Valov V., “Dissertationes Mathematicae”, Diss. Math., 2013, no. 491, 1–120  mathscinet  isi  elib
    7. Bogachev V. Smolyanov O., “Topological Vector Spaces and Their Applications”, Topological Vector Spaces and Their Applications, Springer Monographs in Mathematics, Springer, 2017, 1–456  crossref  mathscinet  zmath  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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