Zobrazeno 1 - 10
of 325
pro vyhledávání: '"54F05"'
Autor:
Abbadini, Marco, Hofmann, Dirk
Compact metric spaces form an important class of metric spaces, but the category that they define lacks many important properties such as completeness and cocompleteness. In recent studies of "metric domain theory" and Stone-type dualities, the more
Externí odkaz:
http://arxiv.org/abs/2408.07039
Autor:
Barría, Sebastián
Let $\mathbb{A}$ and $\mathbb{S}$ denote the double arrow of Alexandroff and the Sorgenfrey line, respectively. We show that for any $n\geq 1$, the space of all unions of at most $n$ closed intervals of $\mathbb{A}$ is not homogeneous. We also prove
Externí odkaz:
http://arxiv.org/abs/2404.13741
Autor:
Richmond, Tom, Wajch, Eliza
A (generalized) topological space is called an iso-dense space if the set of all its isolated points is dense in the space. The main aim of the article is to show in $\mathbf{ZF}$ a new characterization of iso-dense spaces in terms of special quasior
Externí odkaz:
http://arxiv.org/abs/2404.06623
A space is functionally countable if every real-valued continuous function has countable image. A stronger property recently defined by Tkachuk is exponentially separability. We start by studying these properties in GO spaces, where we extend results
Externí odkaz:
http://arxiv.org/abs/2403.15552
Let $X$ be an arbitrary set. Then a topology $t$ on $X$ is said to be completely useful if every upper semicontinuous linear (total) preorder $\precsim$ on $X$ can be represented by an upper semicontinuous real-valued order preserving function. In th
Externí odkaz:
http://arxiv.org/abs/2402.18324
Autor:
Buzyakova, Raushan
We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }
Externí odkaz:
http://arxiv.org/abs/2312.16398
Motivated by results of J. R. Kline and R. L. Moore (1919) that a compact subset of the plane, homeomorphic to a subset of the reals, lies on the arc, we give a purely topological characterisation of compact sets of the reals. This allows us to reduc
Externí odkaz:
http://arxiv.org/abs/2312.13047
Autor:
Gutev, Valentin
In 1951, Ernest Michael wrote a definitive seminal article on hyperspaces raising a general question that became known as the hyperspace selection problem. The present paper contains some aspects of this problem, along with several open questions. Mo
Externí odkaz:
http://arxiv.org/abs/2310.19085
Autor:
Sorin, B. V.
The Roelcke precompactness of transformation groups of discrete spaces and chains in the permutation topology and LOTS in the topology of pointwise convergence is studied. For ultratransitive actions compactifications of transformation groups using t
Externí odkaz:
http://arxiv.org/abs/2310.18570
Autor:
Feng, Ziqin, Gartside, Paul
Every directed set is Tukey equivalent to (a) the family of all compact subsets, ordered by inclusion, of a (locally compact) space, to (b) a neighborhood filter, ordered by reverse inclusion, of a point (of a compact space, and of a topological grou
Externí odkaz:
http://arxiv.org/abs/2309.06523