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<p>In the paper three different characterizations of faces of convex sets belonging to infinite-dimensional real vector spaces are presented. The first one is formulated in terms of generalized semispaces, the second — in terms of compatible total preorders, and the third — in terms of step-affine functions. All three characterizations are equivalent to each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No.&#xa0;1, P. 207–211).</p>

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Characterizations of Faces of Convex Sets in Infinite-dimensional Vector Spaces

  • 期刊论文

  • 发表日期：

    2026年2月9日

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  • Valentin V. Gorokhovik

摘要

In the paper three different characterizations of faces of convex sets belonging to infinite-dimensional real vector spaces are presented. The first one is formulated in terms of generalized semispaces, the second — in terms of compatible total preorders, and the third — in terms of step-affine functions. All three characterizations are equivalent to each other and extend to infinite-dimensional vector spaces the lexicographical characterization of faces established in finite-dimensional settings by Martinez-Legaz J.-E. (Acta Mathematica Vietnamica. 1997. Vol. 22, No. 1, P. 207–211).