Asian Research Journal of Mathematics

On the Subspace Problem for Quasi-normed Spaces

Mangatiana A. Robdera *

Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswan.

*Author to whom correspondence should be addressed.

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Abstract

A definitive positive answer to the so-called proper subspace problem (a.k.a. the atomic space problem) for quasi-normed spaces is given: every infinite dimensional quasi-normed space has a proper closed infinite-dimensional subspace.

Keywords: Quasi-Banach spaces, Hahn-Banach extension property, Minkowski functional, semi-norm

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