DOI: 10.2478/mjpaa-2023-0026 ISSN: 2351-8227

On some generalization of order cancellation law for subsets of topological vector space

Hubert Przybycie
  • Applied Mathematics
  • Control and Optimization
  • Numerical Analysis
  • Analysis
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Abstract

In this paper we generalize a result of R. Urbański from paper [7] which states that for subsets A, B, C of topological vector space X the following implication holds

A + B ⊂ B + C ⇒ A ⊂ C A + B \subset B + C \Rightarrow A \subset C
provided that B is bounded and C is closed and convex. The generalization is given in Theorem 5 where we prove this result for k- convex subsets of a topological vector space. Also we introduce a notion of some abstract like-closure operation for subsets of linear space and we study its connections to order cancellation law.

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