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Classification of semispaces according to their types in infinite-dimensional vector spaces

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Abstract

It is shown that each semispaceC ⊂X naturally generates a relation of complete preorder onX with respect to which the pair (X C, C) is a cut ofX. By identifying the type of the semispace with the type of the cut generated by this semispace, the semispaces are classified according to their types. The obtained classification extends the classification of semispaces in finite-dimensional vector spaces due to Martinez-Legaz and Singer to infinite-dimensional spaces.

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Authors and Affiliations

  1. Institute of Mathematics, Belarussian Academy of Sciences, Belarus

    V. V. Gorokhovik & E. A. Semenkova

Authors
  1. V. V. Gorokhovik
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  2. E. A. Semenkova
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Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 191–198, August, 1998.

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Gorokhovik, V.V., Semenkova, E.A. Classification of semispaces according to their types in infinite-dimensional vector spaces. Math Notes 64, 164–169 (1998). https://doi.org/10.1007/BF02310300

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