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Displaying similar documents to “Realcompactness and spaces of vector-valued functions”

Fixed Points of n-Valued Multimaps of the Circle

Robert F. Brown (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

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A multifunction ϕ: X ⊸ Y is n-valued if ϕ(x) is an unordered subset of n points of Y for each x ∈ X. The (continuous) n-valued multimaps ϕ: S¹ ⊸ S¹ are classified up to homotopy by an integer-valued degree. In the Nielsen fixed point theory of such multimaps, due to Schirmer, the Nielsen number N(ϕ) of an n-valued ϕ: S¹ ⊸ S¹ of degree d equals |n - d| and ϕ is homotopic to an n-valued power map that has exactly |n - d| fixed points. Thus the Wecken property, that Schirmer established...

Set-valued Stratonovich integral

Anna Góralczyk, Jerzy Motyl (2006)

Discussiones Mathematicae Probability and Statistics

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The purpose of the paper is to introduce a set-valued Stratonovich integral driven by a one-dimensional Brownian motion. We discuss the existence of this integral and investigate its properties.

Note on the selection properties of set-valued semimartingales

Mariusz Michta (1996)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.

A fixed point conjecture for Borsuk continuous set-valued mappings

Dariusz Miklaszewski (2002)

Fundamenta Mathematicae

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The main result of this paper is that for n = 3,4,5 and k = n-2, every Borsuk continuous set-valued map of the closed ball in the n-dimensional Euclidean space with values which are one-point sets or sets homeomorphic to the k-sphere has a fixed point. Our approach fails for (k,n) = (1,4). A relevant counterexample (for the homological method, not for the fixed point conjecture) is indicated.