Correction to : “Precompact contraction of metric uniformities and the continuity of $F(t, x)$”

C. J. Himmelberg

Displaying similar documents to “Correction to : “Precompact contraction of metric uniformities and the continuity of $F (t, x)$ ””

Precompact contraction of metric uniformities, and the continuity of $F (t, x)$

C. J. Himmelberg (1973)

Rendiconti del Seminario Matematico della Università di Padova

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Parametrization of Riemann-measurable selections for multifunctions of two variables with application to differential inclusions

Giovanni Anello, Paolo Cubiotti (2004)

Annales Polonici Mathematici

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We consider a multifunction $F : T \times X \to 2^{E}$ , where T, X and E are separable metric spaces, with E complete. Assuming that F is jointly measurable in the product and a.e. lower semicontinuous in the second variable, we establish the existence of a selection for F which is measurable with respect to the first variable and a.e. continuous with respect to the second one. Our result is in the spirit of [11], where multifunctions of only one variable are considered.

CM-Selectors for pairs of oppositely semicontinuous multivalued maps with $_{p}$ -decomposable values

Hôǹg Thái Nguyêñ, Maciej Juniewicz, Jolanta Ziemińska (2001)

Studia Mathematica

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We present a new continuous selection theorem, which unifies in some sense two well known selection theorems; namely we prove that if F is an H-upper semicontinuous multivalued map on a separable metric space X, G is a lower semicontinuous multivalued map on X, both F and G take nonconvex $L_{p} (T, E)$ -decomposable closed values, the measure space T with a σ-finite measure μ is nonatomic, 1 ≤ p < ∞, $L_{p} (T, E)$ is the Bochner-Lebesgue space of functions defined on T with values in a Banach space E, F(x)...

A generalization of boundedly compact metric spaces

Gerald Beer, Anna Di Concilio (1991)

Commentationes Mathematicae Universitatis Carolinae

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A metric space $〈 X, d 〉$ is called a $UC$ space provided each continuous function on $X$ into a metric target space is uniformly continuous. We introduce a class of metric spaces that play, relative to the boundedly compact metric spaces, the same role that $UC$ spaces play relative to the compact metric spaces.

The Banach contraction mapping principle and cohomology

Ludvík Janoš (2000)

Commentationes Mathematicae Universitatis Carolinae

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By a dynamical system $(X, T)$ we mean the action of the semigroup $(ℤ^{+}, +)$ on a metrizable topological space $X$ induced by a continuous selfmap $T : X \to X$ . Let $M (X)$ denote the set of all compatible metrics on the space $X$ . Our main objective is to show that a selfmap $T$ of a compact space $X$ is a Banach contraction relative to some $d_{1} \in M (X)$ if and only if there exists some $d_{2} \in M (X)$ which, regarded as a $1$ -cocycle of the system $(X, T) \times (X, T)$ , is a coboundary.

Median for metric spaces

Nacereddine Belili, Henri Heinich (2001)

Applicationes Mathematicae

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We consider a Köthe space $(, | | \cdot | |_{)}$ of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that ${| | d (X, Y) | |}_{\leq} | | d (X, Z) | |$ for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give...

On convex and *-concave multifunctions

Bożena Piątek (2005)

Annales Polonici Mathematici

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A continuous multifunction F:[a,b] → clb(Y) is *-concave if and only if the inclusion $1 / (t - s) \int_{s}^{t} F (x) d x \subset (F (s) \frac{*}{+} F (t)) / 2$ holds for every s,t ∈ [a,b], s < t.

On the metric reflection of a pseudometric space in ZF

Horst Herrlich, Kyriakos Keremedis (2015)

Commentationes Mathematicae Universitatis Carolinae

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We show: (i) The countable axiom of choice $𝐂𝐀𝐂$ is equivalent to each one of the statements: (a) a pseudometric space is sequentially compact iff its metric reflection is sequentially compact, (b) a pseudometric space is complete iff its metric reflection is complete. (ii) The countable multiple choice axiom $𝐂𝐌𝐂$ is equivalent to the statement: (a) a pseudometric space is Weierstrass-compact iff its metric reflection is Weierstrass-compact. (iii) The axiom of choice $𝐀𝐂$ is equivalent to each...

Selections and representations of multifunctions in paracompact spaces

Alberto Bressan, Giovanni Colombo (1992)

Studia Mathematica

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Let (X,T) be a paracompact space, Y a complete metric space, $F : X \to 2^{Y}$ a lower semicontinuous multifunction with nonempty closed values. We prove that if $T^{+}$ is a (stronger than T) topology on X satisfying a compatibility property, then F admits a $T^{+}$ -continuous selection. If Y is separable, then there exists a sequence $(f_{n})$ of $T^{+}$ -continuous selections such that $F (x) = \bar{f_{n} (x); n \geq 1}$ for all x ∈ X. Given a Banach space E, the above result is then used to construct directionally continuous selections on arbitrary subsets...

Characterizing metric spaces whose hyperspaces are homeomorphic to ℓ₂

T. Banakh, R. Voytsitskyy (2008)

Colloquium Mathematicae

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It is shown that the hyperspace $C l d_{H} (X)$ (resp. $B d d_{H} (X)$ ) of non-empty closed (resp. closed and bounded) subsets of a metric space (X,d) is homeomorphic to ℓ₂ if and only if the completion X̅ of X is connected and locally connected, X is topologically complete and nowhere locally compact, and each subset (resp. each bounded subset) of X is totally bounded.

Displaying similar documents to “Correction to : “Precompact contraction of metric uniformities and the continuity of F ( t , x ) ””

Displaying similar documents to “Correction to : “Precompact contraction of metric uniformities and the continuity of $F (t, x)$ ””