Michael's selection theorem for a mapping definable in an O-minimal structure defined on a set of dimesion 1

Czapla, Małgorzata; Pawłucki, Wiesław

doi:10.12775/tmna.2016.092

Cited by 4 publications

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“…This paper discusses the above problem in the p ‐adic semi‐algebraic context. (Note that similar questions in the context of the reals were discussed in [2, 3, 7, 21]. )…”

Section: Introductionmentioning

confidence: 73%

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On p‐adic semi‐algebraic continuous selections

Thamrongthanyalak

2020

Mathematical Logic Qtrly

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Let E⊆double-struckQpn and T be a set‐valued map from E to Qpm. We prove that if T is p‐adic semi‐algebraic, lower semi‐continuous and T(x) is closed for every x∈E, then T has a p‐adic semi‐algebraic continuous selection. In addition, we include three applications of this result. The first one is related to Fefferman's and Kollár's question on existence of p‐adic semi‐algebraic continuous solution of linear equations with polynomial coefficients. The second one is about the existence of p‐adic semi‐algebraic continuous extensions of continuous functions. The other application is on the characterization of right invertible p‐adic semi‐algebraic continuous functions under the composition.

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“…This paper discusses the above problem in the p ‐adic semi‐algebraic context. (Note that similar questions in the context of the reals were discussed in [2, 3, 7, 21]. )…”

Section: Introductionmentioning

confidence: 73%

“…This paper discusses the above problem in the p-adic semi-algebraic context. (Note that similar questions in the context of the reals were discussed in [2,3,7,21].) Throughout, let p be a fixed prime number, Q p be the set of p-adic numbers with the p-adic valuation v : Q p → Z ∪ {+∞} and E denote a subset of some Q n p .…”

Section: Introductionmentioning

confidence: 96%

On p‐adic semi‐algebraic continuous selections

Thamrongthanyalak

2020

Mathematical Logic Qtrly

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“…M. Czapla and W. Paw lucki [3] proved 3.7 (M. Czapla, W. Paw lucki [3]). Let T : E ⇒ R n be a definable and lower semicontinuous set-valued map with nonempty connected values and dim E = 1.…”

Section: For Allmentioning

confidence: 96%

Definable continuous selections of set-valued maps in o-minimal expansions of the real field

Sokantika

Thamrongthanyalak

2017

Bull. Polish Acad. Sci. Math.

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“…In [4], M. Czapla and W. Pawłucki proved the following theorem: such that f ⊆ T 0 and for every x ∈ E, T 0 (x) is connected. By Lemma 2.6, let C be a cell decomposition of E such that T 0 C is lower semi-continuous for every…”

Section: Existence Of Selections and Definable Selectionsmentioning

confidence: 99%

“…(M. Czapla and W. Pawłucki[4]). Let T : E ⇒ m be a definable and lower semi-continuous set-valued map with nonempty connected values and dim E = 1.…”

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confidence: 99%

Selection problems in O-minimal structures

Sokantika

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In this dissertation, we improve the Definable Michael's Selection Theorem in o-minimal expansions of real closed fields. Then applications of this theorem are established; for instance, we prove the following statement: Let be an o-minimal expansion of and T be a definable set-valued map where n = 1 or m=1. If T has a continuous selection, then T has a definable continuous selection. Moreover, we prove the statement: Let be an o-minimal expansion of a real closed field and be a closed subset of Rn. If T: E --> Rm is a definable continuous set-valued map and T is bounded for each in the boundary of E, then T has a definable continuous extension.

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Michael's selection theorem for a mapping definable in an O-minimal structure defined on a set of dimesion 1

Cited by 4 publications

References 0 publications

On p‐adic semi‐algebraic continuous selections

On p‐adic semi‐algebraic continuous selections

Definable continuous selections of set-valued maps in o-minimal expansions of the real field

Selection problems in O-minimal structures

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