An Embedding Theorem for Unbounded Convex Sets in a Banach Space

Bielawski, Jakub; Tabor, Jacek

doi:10.1515/dema-2009-0405

Cited by 6 publications

(15 citation statements)

References 1 publication

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“…In this section we prove order cancellation law for topological vector space where we cancel by closed and convex sets . These results generalize theorems obtained by and Tabor, Bielawski in [3].…”

Section: Assymptotic and Recession Conessupporting

confidence: 91%

“…The following theorems follow from the above considerations and Section 2. Tabor and Bielawski [3] proved a version of order cancellation law for closed convex sets having finite Hausdorff distance from a fixed convex cone V in a normed space X. Theorem 5.5 is another version of order cancellation law which generalizes to topological spaces a result obtained by Tabor and Bielawski.…”

Section: Order Cancellation Law In Topological Vector Spacesmentioning

confidence: 85%

“…In this section, we prove the order cancellation law for, respectively, bounded and convex elements in ordered semigroups. The results of this section will be applied in Section 5 where we give a generalization of Bielawski-Tabor result [3] to topological vector spaces.…”

Section: Cancellation Law In An Ordered Semigroup With An Operator Of...mentioning

confidence: 99%

“…He also embedded C V (R n ) into a topological vector space (but not into a normed space). Bielawski and Tabor [3] restricted the family C V (X), where X is a normed vector space to such closed convex sets A that the Hausdorff distance d H (A, V ) is finite. It enabled them to embed restricted C V (X) into a normed vector space, generalizing in this case the Rådström's result [24].…”

Section: Introductionmentioning

confidence: 99%

“…(see Theorem 2 in[3].) Let X be a Banach space, V a closed convex cone in X, d H a Hausdorff distance and…”

mentioning

confidence: 99%

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Order cancellation law in the family of bounded convex sets

Grzybowski

Urbański

2019

J Glob Optim

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In this paper generalize Robinson's version of an order cancellation law for subsets of vector spaces in which we cancel by unbounded sets. We introduce the notion of weakly narrow sets in normed spaces, study their properties and prove the order cancellation law where the canceled set is weakly narrow. Also we prove the order cancellation law for closed convex subsets of topological vector space where the canceled set has bounded Hausdorff-like distance from its recession cone. We topologically embed the semigroup of closed convex sets sharing a recession cone having bounded Hausdorff-like distance from it into a topological vector space. This result extends Bielawski and Tabor's generalization of Rådström theorem.

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Section: Assymptotic and Recession Conessupporting

confidence: 91%

Section: Order Cancellation Law In Topological Vector Spacesmentioning

confidence: 85%

Section: Cancellation Law In An Ordered Semigroup With An Operator Of...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…(see Theorem 2 in[3].) Let X be a Banach space, V a closed convex cone in X, d H a Hausdorff distance and…”

mentioning

confidence: 99%

See 3 more Smart Citations

Order cancellation law in the family of bounded convex sets

Grzybowski

Urbański

2019

J Glob Optim

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A t-norm embedding theorem for fuzzy sets

Bielawski

Tabor

2012

Fuzzy Sets and Systems

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Order Cancellation Law in a Semigroup of Closed Convex Sets

Grzybowski¹,

Przybycień²

2022

Taiwanese J. Math.

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In this paper we generalize Robinson's version of an order cancellation law in which some unbounded subsets of a vector space are cancellative elements. We introduce the notion of weakly narrow sets in normed spaces, study their properties and prove the order cancellation law where the canceled set is weakly narrow. Also, we prove the order cancellation law for closed convex subsets of topological vector space where the canceled set has bounded Hausdorff-like distance from its recession cone. We topologically embed the semigroup of closed convex sets sharing a recession cone having bounded Hausdorff-like distance from it into a topological vector space. This result extends Bielawski and Tabor's generalization of Rådström theorem.

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An Embedding Theorem for Unbounded Convex Sets in a Banach Space

Cited by 6 publications

References 1 publication

Order cancellation law in the family of bounded convex sets

Order cancellation law in the family of bounded convex sets

A t-norm embedding theorem for fuzzy sets

Order Cancellation Law in a Semigroup of Closed Convex Sets

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