Zobrazeno 1 - 10
of 301
pro vyhledávání: '"54c20"'
Autor:
Gutev, Valentin
The classical McShane-Whitney extension theorem for Lipschitz functions is refined by showing that for a closed subset of the domain, it remains valid for any interval of the real line. This result is also extended to the setting of locally (pointwis
Externí odkaz:
http://arxiv.org/abs/2411.17825
Autor:
Gutev, Valentin
The paper contains a very simple proof of the classical Hasumi's theorem that each usco mapping defined on an extremally disconnected space has a continuous selection. The paper also contains a very simple proof of a recent result about extension of
Externí odkaz:
http://arxiv.org/abs/2409.09490
Autor:
Chen, Deliang
The Machado--Bishop theorem for weighted vector-valued functions vanishing at infinity has been extensively studied. In this paper, we give an analogue of Machado's distance formula for bounded weighted vector-valued functions. A number of applicatio
Externí odkaz:
http://arxiv.org/abs/2407.19925
This is a survey of recent and classical results concerning various types of homogeneity, such as n-homogeneity, discrete homogeneity, and countable dense homogeneity. Some new results are also presented, and several problems are posed.
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Externí odkaz:
http://arxiv.org/abs/2407.11815
Autor:
Liseev, Mikhail Yourievich
In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for mappings is
Externí odkaz:
http://arxiv.org/abs/2406.08061
In the paper, we address the following problem, often encountered in geometric constructions: having defined an orientation preserving diffeomorphism in a number of `patches' on a manifold $\mathcal{M}$, can we extend it to a diffeomorphism of the wh
Externí odkaz:
http://arxiv.org/abs/2404.13508
Autor:
Serraille, Baptiste
In this paper, we present a $C^0$-fragmentation property for Hamiltonian diffeomorphisms. More precisely, it is known that for a given open covering $\mathcal{U}$ of a compact symplectic surface we can write each $C^0$-small enough Hamiltonian diffeo
Externí odkaz:
http://arxiv.org/abs/2403.15767
Motivated by manifold-constrained homogenization problems, we construct an extension operator for Sobolev functions defined on a perforated domain and taking values in a compact, connected $C^2$-manifold without boundary. The proof combines a by now
Externí odkaz:
http://arxiv.org/abs/2403.11690
Autor:
Backus, Aidan, Ze-An, Ng
Let $\Gamma$ be a closed subset of a complete Riemannian manifold $M$ of dimension $\geq 2$, let $f: M \to N$ be a Lipschitz map to a complete Riemannian manifold $N$, and let $\psi$ be a continuous function which dominates the local Lipschitz consta
Externí odkaz:
http://arxiv.org/abs/2403.07702
Autor:
Ciosmak, Krzysztof J.
Let $X$ be a subset of a Hilbert space. We prove that if $v\colon X\to \mathbb{R}^m$ is such that \begin{equation*} \Big\lVert v(x)-\sum_{i=1}^m t_iv(x_i)\Big\rVert\leq \Big\lVert x-\sum_{i=1}^m t_ix_i\Big\rVert \end{equation*} for all $x,x_1,\dotsc,
Externí odkaz:
http://arxiv.org/abs/2402.14699