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pro vyhledávání: '"Lipham, David Sumner"'
Autor:
Lipham, David Sumner
E.D. Tymchatyn constructed a hereditarily locally connected continuum which can be approximated by a sequence of mutually disjoint arcs. We show the example re-opens a conjecture of G.T. Seidler and H. Kato about continua which admit positive entropy
Externí odkaz:
http://arxiv.org/abs/1910.00563
Autor:
Lipham, David Sumner
Publikováno v:
Ergodic Theory and Dynamical Systems (2019)
We study topological properties of the escaping endpoints and fast escaping endpoints of the Julia set of complex exponential $\exp(z)+a$ when $a\in (-\infty,-1)$. We show neither space is homeomorphic to the whole set of endpoints. This follows from
Externí odkaz:
http://arxiv.org/abs/1908.10985
Autor:
Lipham, David Sumner
Publikováno v:
Proc. Amer. Math. Soc. 148 (2020)
We construct two connected plane sets which can be embedded into rational curves. The first is a biconnected set with a dispersion point. It answers a question of Joachim Grispolakis. The second is indecomposable. Both examples are completely metriza
Externí odkaz:
http://arxiv.org/abs/1904.04463
Autor:
Lipham, David Sumner
Publikováno v:
Topology and its Applications 260 (2019)
Suppose $Y$ is a continuum, $x\in Y$, and $X$ is the union of all nowhere dense subcontinua of $Y$ containing $x$. Suppose further that there exists $y\in Y$ such that every connected subset of $X$ limiting to $y$ is dense in $X$. And, suppose $X$ is
Externí odkaz:
http://arxiv.org/abs/1806.10828
Autor:
Lipham, David Sumner
We show that every connected set $X$ which is irreducible between two points $a$ and $b$ embeds into the Hilbert cube in a way that $X\cup \{c\}$ is irreducible between $a$ and $b$ for every point $c$ in the closure of $X$. Also, a connected set $X$
Externí odkaz:
http://arxiv.org/abs/1804.05440
Autor:
Lipham, David Sumner
Publikováno v:
Topology and its Applications 243 (2018)
The following is an open problem in topology: Determine whether the Stone-\v{C}ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and sufficient in orde
Externí odkaz:
http://arxiv.org/abs/1703.06862
Autor:
Lipham, David Sumner
Publikováno v:
Fundamenta Mathematicae 240 (2018)
A connected topological space is said to be widely-connected if each of its non-degenerate connected subsets is dense in the entire space. The object of this paper is the construction of widely-connected subsets of the plane. We give a completely met
Externí odkaz:
http://arxiv.org/abs/1608.00292
Autor:
Lipham, David Sumner
Publikováno v:
In Topology and its Applications 15 June 2019 260:104-115
Autor:
Lipham, David Sumner
The following is an open problem in topology: Determine whether the Stone-��ech compactification of a widely-connected space is necessarily an indecomposable continuum. Herein we describe properties of $X$ that are necessary and sufficient in ord
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7de1952a58b7ae773c730cb6f2ff74b1