Zobrazeno 1 - 10
of 84
pro vyhledávání: '"Tymchatyn, E. D."'
For a topologically complete space $X$ and a family of closed covers $\mathcal A$ of $X$ satisfying a "local refinement condition" and a "completeness condition," we give a construction of an inverse system $\mathbf{ N}_{\mathcal A}$ of simplicial co
Externí odkaz:
http://arxiv.org/abs/1907.11531
Let $\Omega$ be a connected open set in the plane and $\gamma: [0,1] \to \overline{\Omega}$ a path such that $\gamma((0,1)) \subset \Omega$. We show that the path $\gamma$ can be ``pulled tight'' to a unique shortest path which is homotopic to $\gamm
Externí odkaz:
http://arxiv.org/abs/1903.06737
Let $A$ be any plane set. It is known that a holomorphic motion $h: A \times \mathbb{D} \to \mathbb{C}$ always extends to a holomorphic motion of the entire plane. It was recently shown that any isotopy $h: X \times [0,1] \to \mathbb{C}$, starting at
Externí odkaz:
http://arxiv.org/abs/1808.05601
For sufficiently tame paths in $\mathbb{R}^n$, Euclidean length provides a canonical parametrization of a path by length. In this paper we provide such a parametrization for all continuous paths. This parametrization is based on an alternative notion
Externí odkaz:
http://arxiv.org/abs/1301.6070
Autor:
Blokh, Alexander M., Fokkink, Robbert J., Mayer, John C., Oversteegen, Lex G., Tymchatyn, E. D.
Publikováno v:
Memoirs of the AMS, vol. 224 (2013), no. 1053
We present proofs of basic results, including those developed by Harold Bell, for the plane fixed point problem: does every map of a non-separating plane continuum have a fixed point? Some of these results had been announced much earlier by Bell but
Externí odkaz:
http://arxiv.org/abs/1004.0214
Autor:
Oversteegen, Lex G., Tymchatyn, E. D.
In this paper we solve the following problem in the affirmative: Let $Z$ be a continuum in the plane $\complex$ and suppose that $h:Z\times [0,1]\to\complex$ is an isotopy starting at the identity. Can $h$ be extended to an isotopy of the plane? We w
Externí odkaz:
http://arxiv.org/abs/0811.0364
Publikováno v:
Proceedings of the American Mathematical Society. Volume 136, Number 11, November 2008, Pages 4045--4055.
We show that a plane continuum X is indecomposable iff X has a sequence (U_n) of not necessarily distinct complementary domains satisfying what we call the double-pass condition: If one draws an open arc A_n in each U_n whose ends limit into the boun
Externí odkaz:
http://arxiv.org/abs/0805.3320
In this paper we present proofs of basic results, including those developed so far by H. Bell, for the plane fixed point problem. Some of these results had been announced much earlier by Bell but without accessible proofs. We define the concept of th
Externí odkaz:
http://arxiv.org/abs/0805.1184
Autor:
Tymchatyn, E. D., Valov, V.
Several authors have recently attempted to show that the intersection of three simply connected subcontinua of the plane is simply connected provided it is non-empty and the intersection of each two of the continua is path connected. In this note we
Externí odkaz:
http://arxiv.org/abs/math/0409349
Autor:
Tymchatyn, E. D., Zarichnyi, M.
We consider the question of simultaneous extension of (pseudo)metrics defined on nonempty closed subsets of a compact metrizable space. The main result is a counterpart of the result due to K\"unzi and Shapiro for the case of extension operators of p
Externí odkaz:
http://arxiv.org/abs/math/0211215