The strongest vector space topology is locally convex on separable linear subspaces

W. Żelazko

Annales Polonici Mathematici (1997)

  • Volume: 66, Issue: 1, page 275-282
  • ISSN: 0066-2216

Abstract

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Let X be a real or complex vector space equipped with the strongest vector space topology τ m a x . Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.

How to cite

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W. Żelazko. "The strongest vector space topology is locally convex on separable linear subspaces." Annales Polonici Mathematici 66.1 (1997): 275-282. <http://eudml.org/doc/269973>.

@article{W1997,
abstract = {Let X be a real or complex vector space equipped with the strongest vector space topology $τ_\{max\}$. Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.},
author = {W. Żelazko},
journal = {Annales Polonici Mathematici},
keywords = {topological vector spaces; locally pseudoconvex spaces; locally convex subspaces; strongest vector space topology; strongest locally convex topology; locally -convex; locally pseudoconvex; (un-) countable dimension; pseudoconvex},
language = {eng},
number = {1},
pages = {275-282},
title = {The strongest vector space topology is locally convex on separable linear subspaces},
url = {http://eudml.org/doc/269973},
volume = {66},
year = {1997},
}

TY - JOUR
AU - W. Żelazko
TI - The strongest vector space topology is locally convex on separable linear subspaces
JO - Annales Polonici Mathematici
PY - 1997
VL - 66
IS - 1
SP - 275
EP - 282
AB - Let X be a real or complex vector space equipped with the strongest vector space topology $τ_{max}$. Besides the result announced in the title we prove that X is uncountable-dimensional if and only if it is not locally pseudoconvex.
LA - eng
KW - topological vector spaces; locally pseudoconvex spaces; locally convex subspaces; strongest vector space topology; strongest locally convex topology; locally -convex; locally pseudoconvex; (un-) countable dimension; pseudoconvex
UR - http://eudml.org/doc/269973
ER -

References

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  1. [1] S. Banach, Théorie des Opérations Linéaires, Warszawa, 1932. Zbl0005.20901
  2. [2] N. Dunford and J. T. Schwartz, Linear Operators I, Interscience, New York, 1958. 
  3. [3] H. Jarchow, Locally Convex Spaces, Teubner, Stuttgart, 1981. Zbl0466.46001
  4. [4] A. Grothendieck, Topological Vector Spaces, Gordon and Breach, New York, 1973. 
  5. [5] A. Kokk and W. Żelazko, On vector spaces and algebras with maximal locally pseudoconvex topologies, Studia Math. 112 (1995), 195-201. Zbl0837.46037
  6. [6] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969. Zbl0179.17001
  7. [7] G. Köthe, Topological Vector Spaces II, Springer, Berlin, 1979. Zbl0417.46001
  8. [8] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa, 1972. 
  9. [9] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971. 
  10. [10] L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Math. 230, Springer, 1971. Zbl0225.46001
  11. [11] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New York, 1978. Zbl0395.46001

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