<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In this paper we generalize a result of R. Urbański from paper [7] which states that for subsets <italic>A</italic>, <italic>B</italic>, <italic>C</italic> of topological vector space <italic>X</italic> the following implication holds 
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2023-0026_eq_001.png"></graphic>
<math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mrow><mi>A</mi><mo>+</mo><mi>B</mi><mo>⊂</mo><mi>B</mi><mo>+</mo><mi>C</mi><mo>⇒</mo><mi>A</mi><mo>⊂</mo><mi>C</mi></mrow></math>
<tex-math>A + B \subset B + C \Rightarrow A \subset C</tex-math>
</alternatives>
</disp-formula>
 provided that <italic>B</italic> is bounded and <italic>C</italic> is closed and convex. The generalization is given in Theorem 5 where we prove this result for <italic>k</italic>- 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.</p>
</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.

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

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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...

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

Publié en ligne: 29 sept. 2023

Pages: 378 - 382

Reçu: 27 juin 2023

Accepté: 27 sept. 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0026

Mots clés
convex sets, Minkowski addition of sets, cancellation law

© 2023 Hubert Przybycie, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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

Publié en ligne: 29 sept. 2023

Pages: 378 - 382

Reçu: 27 juin 2023

Accepté: 27 sept. 2023

DOI: https://doi.org/10.2478/mjpaa-2023-0026

Mots clésconvex sets, Minkowski addition of sets, cancellation law

© 2023 Hubert Przybycie, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Mots clés
convex sets, Minkowski addition of sets, cancellation law