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

Annales Polonici Mathematici (1997)

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

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topW. 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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- [4] A. Grothendieck, Topological Vector Spaces, Gordon and Breach, New York, 1973.
- [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] G. Köthe, Topological Vector Spaces I, Springer, Berlin, 1969. Zbl0179.17001
- [7] G. Köthe, Topological Vector Spaces II, Springer, Berlin, 1979. Zbl0417.46001
- [8] S. Rolewicz, Metric Linear Spaces, PWN, Warszawa, 1972.
- [9] H. H. Schaefer, Topological Vector Spaces, Springer, New York, 1971.
- [10] L. Waelbroeck, Topological Vector Spaces and Algebras, Lecture Notes in Math. 230, Springer, 1971. Zbl0225.46001
- [11] A. Wilansky, Modern Methods in Topological Vector Spaces, McGraw-Hill, New York, 1978. Zbl0395.46001

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