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Zbl 1101.46017
Garc{\'\i}a-Raffi, L.M.
Compactness and finite dimension in asymmetric normed linear spaces. (English)
[J] Topology Appl. 153, No. 5-6, 844-853 (2005). ISSN 0166-8641

Summary: We describe the compact sets of any asymmetric normed linear space. After that, we focus our attention on finite-dimensional asymmetric normed linear spaces. In this case, we establish the equivalence between the $T_{1}$ separation axiom and normable spaces. An asymmetric version of the Riesz theorem about the compactness of the unit ball is proved. We also prove that the Heine-Borel theorem characterizes finite-dimensional asymmetric normed linear spaces that satisfy the $T_{2}$ separation axiom. Finally, we focus our attention on the $T_{0}$ separation axiom and results that are related to the dual $p$-complexity spaces.

MSC 2000:: *46B99 Normed linear spaces and Banach spaces
54E50 Complete metric spaces
54H99 Connections of general topology with other structures

Keywords: asymmetric normed linear space; compactness; finite dimension

Cited in: Zbl 1185.46001

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