Asymptotic property C of the countable direct sum of uniformly discrete $0$-hyperbolic spaces

可数函数平衡群

Countable uniformly discrete sets in functionally balanced groups

该研究回答了拓扑群领域的两个问题，证明可数豪斯多夫函数平衡群是平衡群，还得到FSIN群的相关离散族性质，明确了问题间的逻辑关系。

On uniformly continuous maps between function spaces

In this paper we develop a technique of constructing uni- formly continuous maps between function spaces Cp(X) endowed with the pointwise topology. We prove that if a space X is compact metrizable and strongly countable-dimensional, then there exists a uniformly contin- uous surjection from Cp([0,1]) onto Cp(X). We provide a partial result concerning the reverse implication. We also show that, for every infinite Polish zero-dimensional space X, the spaces Cp(X) and Cp(X) x Cp(X) are uniformly homeomorphic. This partially answers two questions posed by Krupski and Marciszewski.

On the Baire space of $ω_1$-strongly compact weight

We prove that on the Baire space $(D^κ,π)$, $κ\geq ω_0$ where $D$ is a uniformly discrete space having $ω_1$-strongly compact cardinal and $π$ denotes the product uniformity on $D^κ$, there exists a $z_u$-filter $\mathcal{F}$ being Cauchy for the uniformity $eπ$ having as a base all the countable uniform partitions of $(D^κ,π)$, and failing the countable intersection property. This fact is equivalent to the existence of a non-vanishing real-valued uniformly continuous function $f$ on $D^κ$ for which the inverse function $g=1/f$ cannot be continuously extended to the completion of $(D^{κ_0},eπ)…

无界双曲空间上的通用一致连续映射

Generic uniformly continuous mappings on unbounded hyperbolic spaces

本文在无界双曲空间中研究连续模受给定凹函数控制的一致连续自映射空间，证明在 Baire 范畴意义下通用映射的连续模恰为该函数，并讨论有界映射与逐点收敛拓扑下的相关结果。