Completeness, precompactness and compactness in finite-dimensional asymmetrically normed lattices. (English) Zbl 1290.46003
Summary: If \((X,\|\cdot\|)\) is a real normed lattice, then \(p(x)=\| x^+\|\) defines an asymmetric norm on \(X\). We characterise the left-\(K\) sequentially complete, precompact and compact subsets of \((\mathbb R^m,p)\).
MSC:
| 46A40 | Ordered topological linear spaces, vector lattices |
| 46B42 | Banach lattices |
| 54E25 | Semimetric spaces |
| 46B50 | Compactness in Banach (or normed) spaces |
Keywords:
finite-dimensional asymmetrically normed lattice; left-\(K\) sequential completeness; precompactness; compactnessReferences:
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