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pro vyhledávání: '"van Mill, Jan"'
We show that in the class of Lindel\"of \v{C}ech-complete spaces the property of being $C$-embedded is quite well-behaved. It admits a useful characterization that can be used to show that products and perfect preimages of $C$-embedded spaces are aga
Externí odkaz:
http://arxiv.org/abs/2404.19703
Sets on the boundary of a complementary component of a continuum in the plane have been of interest since the early 1920's. Curry and Mayer defined the buried points of a plane continuum to be the points in the continuum which were not on the boundar
Externí odkaz:
http://arxiv.org/abs/2401.10206
Autor:
Juhász, István, van Mill, Jan
If $X$ is a topological space and $Y$ is any set then we call a family $\mathcal{F}$ of maps from $X$ to $Y$ nowhere constant if for every non-empty open set $U$ in $X$ there is $f \in \mathcal{F}$ with $|f[U]| > 1$, i.e. $f$ is not constant on $U$.
Externí odkaz:
http://arxiv.org/abs/2312.12257
Autor:
Juhász, István, van Mill, Jan
We show that every infinite crowded space can be mapped onto a homogeneous space of countable weight, and that there is a homogeneous space of weight continuum that cannot be mapped onto a homogeneous space of uncountable weight strictly less than co
Externí odkaz:
http://arxiv.org/abs/2310.20359
We provide partial solutions to two problems posed by Shehtman concerning the modal logic of the \v{C}ech-Stone compactification of an ordinal space. We use the Continuum Hypothesis to give a finite axiomatization of the modal logic of $\beta(\omega^
Externí odkaz:
http://arxiv.org/abs/2308.13684
We investigate closed copies of~$\mathbb{N}$ in powers of~$\mathbb{R}$ with respect to $C^*$- and $C$-embedding. We show that $\mathbb{R}^{\omega_1}$ contains closed copies of~$\mathbb{N}$ that are not $C^*$-embedded.
Comment: Version 2: some co
Comment: Version 2: some co
Externí odkaz:
http://arxiv.org/abs/2307.07223
Autor:
Juhász, István, Van Mill, Jan
The set $dd(X)$ of densities of all dense subspaces of a topological space $X$ is called the double density spectrum of $X$. In this note we present a couple of results that imply $\lambda \in dd(X)$, provided that $X$ is a compact space and $\lambda
Externí odkaz:
http://arxiv.org/abs/2302.02348
Publikováno v:
Topology Proceedings 62 (2023), 205-216 (e-published on 25-08-2023)
We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of the space of natural numbers.
Comment: Version 2: corrections after referee report. One questi
Comment: Version 2: corrections after referee report. One questi
Externí odkaz:
http://arxiv.org/abs/2211.16545
Autor:
Hart, Klaas Pieter, van Mill, Jan
Publikováno v:
Topology and its Applications 2024
This is an update on, and expansion of, our paper Open problems on $\beta\omega$ in the book Open Problems in Topology.
Comment: New version, much reworked. 2024-02-01: version after comments from the referee. 2024-08-24: added classification, k
Comment: New version, much reworked. 2024-02-01: version after comments from the referee. 2024-08-24: added classification, k
Externí odkaz:
http://arxiv.org/abs/2205.11204
It is an interesting, maybe surprising, fact that different dense subspaces of even "nice" topological spaces can have different densities. So, our aim here is to investigate the set of densities of all dense subspaces of a topological space $X$ that
Externí odkaz:
http://arxiv.org/abs/2109.10823