# Simple construction of spaces without the Hahn-Banach extension property

Commentationes Mathematicae Universitatis Carolinae (1992)

- Volume: 33, Issue: 4, page 623-624
- ISSN: 0010-2628

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topKąkol, Jerzy. "Simple construction of spaces without the Hahn-Banach extension property." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 623-624. <http://eudml.org/doc/247361>.

@article{Kąkol1992,

abstract = {An elementary construction for an abundance of vector topologies $\xi $ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )^\{\prime \}$ separates points of $E$ from zero is given.},

author = {Kąkol, Jerzy},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Hahn-Banach extension property; topological vector space; construction of spaces without the Hahn-Banach extension property; topological dual separates points; vector topologies},

language = {eng},

number = {4},

pages = {623-624},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Simple construction of spaces without the Hahn-Banach extension property},

url = {http://eudml.org/doc/247361},

volume = {33},

year = {1992},

}

TY - JOUR

AU - Kąkol, Jerzy

TI - Simple construction of spaces without the Hahn-Banach extension property

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1992

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 33

IS - 4

SP - 623

EP - 624

AB - An elementary construction for an abundance of vector topologies $\xi $ on a fixed infinite dimensional vector space $E$ such that $(E,\xi )$ has not the Hahn-Banach extension property but the topological dual $(E,\xi )^{\prime }$ separates points of $E$ from zero is given.

LA - eng

KW - Hahn-Banach extension property; topological vector space; construction of spaces without the Hahn-Banach extension property; topological dual separates points; vector topologies

UR - http://eudml.org/doc/247361

ER -

## References

top- Duren P.L., Romberg R.C., Shields A.L., Linear functionals in ${H}^{p}$-spaces with $0<p<1$, J. Reine Angew. Math. 238 (1969), 32-60. (1969) MR0259579
- Kalton N.J., Basic sequences in $F$-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151-167. (1974) Zbl0296.46010MR0415259
- Kakol J., Nonlocally convex spaces and the Hahn-Banach extension property, Bull. Acad. Polon. Sci. 33 (1985), 381-393. (1985) Zbl0588.46004MR0821575
- Klee V., Exotic topologies for linear spaces, Proc. Symposium on General Topology and its Relations to Modern Algebra, Prague, 1961. Zbl0111.10701MR0154088
- Shapiro J.H., Examples of proper closed weakly dense subspaces in non-locally convex $F$-spaces, Israel J. Math. 7 (1969), 369-380. (1969) Zbl0202.39303MR0257696
- Wilansky A., Topics in Functional Analysis, Springer Verlag 45 (1967). Zbl0156.36103MR0223854

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