Zobrazeno 1 - 10
of 13 743
pro vyhledávání: '"General topology"'
Autor:
Liang, Bingbing, Yan, Kesong
We investigate the dynamical property of the naive mean dimension for continuous actions of any countable group on compact metrizable spaces. It is shown that naive mean dimension serves as an upper bound of sofic mean dimension for actions of noname
Externí odkaz:
http://arxiv.org/abs/2410.12528
In this paper we have introduced the notion of $\mathcal{I}$-sparse set in the space of reals and explored some properties of the family of $\mathcal{I}$-sparse sets. Thereafter we have induced a topology namely $\mathcal{I}$-sparse set topology in t
Externí odkaz:
http://arxiv.org/abs/2410.12503
Autor:
Wu, Guojun, Yao, Wei
With a commutative integral quantale $L$ as the truth value table, this study focuses on the characterizations of the sobriety of stratified $L$-convex spaces, as introduced by Liu and Yue in 2024. It is shown that a stratified sober $L$-convex space
Externí odkaz:
http://arxiv.org/abs/2410.09853
Through this paper we will modify some of the results of [1], [5], [15], [28], [29], [31], [32] and consequently give the modified results.
Externí odkaz:
http://arxiv.org/abs/2410.09791
Autor:
Brian, Will, Farah, Ilijas
A trivial automorphism of the Boolean algebra $\mathcal P(\mathbb N) / \mathrm{Fin}$ is an automorphism induced by the action of some function $\mathbb N \rightarrow \mathbb N$. In models of forcing axioms all automorphisms are trivial, and therefore
Externí odkaz:
http://arxiv.org/abs/2410.08789
Autor:
Keith, Jonathan M.
Upper asymptotic density induces a pseudometric on the power set of the natural numbers, with respect to which $P(\mathbb{N})$ is complete. The collection $D$ of sets with asymptotic density is closed in this pseudometric, and closed subsets of $D$ a
Externí odkaz:
http://arxiv.org/abs/2410.06559
Autor:
Leibo, I. M.
The coincidence of the $\Ind$ and $\dim$ dimensions for first countable paracompact $\sigma$-spaces is proved. This gives a positive answer to A. V. Arkhangel'skii's question of whether the dimensions $\ind X$, $\Ind X$, and $\dim X$ are equal for fi
Externí odkaz:
http://arxiv.org/abs/2410.03469
Autor:
Hoganson, Hannah, Zomback, Jenna
We demonstrate that the proper homotopy equivalence relation for locally finite graphs is Borel complete. Furthermore, among the infinite graphs, there is a comeager equivalence class. As corollaries, we obtain the analogous results for the homeomorp
Externí odkaz:
http://arxiv.org/abs/2410.00901
For every $n \geq 2$, let $K_k^n$ denote the hyperspace of all $k$-dimensional closed convex subsets of the Euclidean space $R^n$ endowed with the Atouch-Wets topology. Let $ K_{k,b}^n$ be the subset of $K_k^n$ consisting of all $k$-dimensional compa
Externí odkaz:
http://arxiv.org/abs/2410.00839
Autor:
Tsaban, Boaz
We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental theorems in t
Externí odkaz:
http://arxiv.org/abs/2409.20518