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A General Separation Theorem For Various Structures

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Abstract

There are several important separation theorems in various areas; for example, theorems of Gordan, Stone, Mazur, Hahn–Banach, etc. In this paper, we give a general treatment, in ZFC, of separation results with several examples in old and new settings. In order to achieve some uniformity of the treatment, we define the notion of a solid operator that leads to the notion of separation. We also characterize those topological spaces for which the closure of a set is a solid operator. Further, we prove a separation theorem for solid operators which we will use to characterize those graphic matroids whose span is a solid operator. We also use the separation theorem to prove a theorem of Páles.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Queensborough Community College, Bayside, NY, 11364, USA

    F. Jordan

  2. Department of Mathematics, Western Illinois University, Macomb, Illinois, 61455, USA

    I. Kalantari

  3. Department of Mathematics, Medgar Evers College, CUNY, Brooklyn, NY, 11225, USA

    H. Pajoohesh

Authors
  1. F. Jordan
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  2. I. Kalantari
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  3. H. Pajoohesh
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Correspondence to F. Jordan.

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Jordan, F., Kalantari, I. & Pajoohesh, H. A General Separation Theorem For Various Structures. Acta Math. Hungar. 162, 345–363 (2020). https://doi.org/10.1007/s10474-020-01062-1

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  • DOI: https://doi.org/10.1007/s10474-020-01062-1

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