Building suitable sets for locally compact groups by means of continuous selections

局部紧强拓扑gyrogroup中合适集的存在性

The existence of suitable sets in locally compact strongly topological gyrogroups

本文证明了每个局部紧强拓扑gyro群都存在一个合适集，解决了Lin等人提出的问题。

Fixed points and selections of multifunctions on spaces with convexity

We provide theorems containnig both Kakutani and Browder fixed points theorems as immediate corollaries, as well as Michael and Browder selection theorems. For this purpose we introduce convex structures more general than those of locally convex and non-locally convex topological vector spaces or generalized convexity structures due to Michael, Van de Vel and Horvath.

Notes on linearly H-closed spaces and od-selection principles

A space is called linearly H-closed iff any chain cover possesses a dense member. This property lies strictly between feeble compactness and H-closedness. While regular H-closed spaces are compact, there are linearly H-closed spaces which are even collectionwise normal and Fréchet-Urysohn. We give examples in other classes, and ask whether there is a first countable normal linearly H-closed non-compact space in ZFC. We show that PFA implies a negative answer if the space is moreover either locally separable or locally compact and locally ccc. Ostaszewski space (built with $\diamondsuit$) is an…

近似群的广义局部紧致模型

Generalized locally compact models for approximate groups

利用拓扑动力学证明任意近似子群广义可定义局部紧致模型的存在性，构造更简单，还证明了其通用性，给出了可定义群的可定义泛型子集结构信息。

Hyperspace of convex compacta of nonmetrizable compact convex subspaces of locally convex spaces

Our main result states that the hyperspace of convex compact subsets of a compact convex subset $X$ in a locally convex space is an absolute retract if and only if $X$ is an absolute retract of weight $\leω_1$. It is also proved that the hyperspace of convex compact subsets of the Tychonov cube $I^{ω_1}$ is homeomorphic to $I^{ω_1}$. An analogous result is also proved for the cone over $I^{ω_1}$. Our proofs are based on analysis of maps of hyperspaces of compact convex subsets, in particular, selection theorems for such maps are proved.

Topological entropy in totally disconnected locally compact groups

Let $G$ be a topological group, let $ϕ$ be a continuous endomorphism of $G$ and let $H$ be a closed $ϕ$-invariant subgroup of $G$. We study whether the topological entropy is an additive invariant, that is, $$h_{top}(ϕ)=h_{top}(ϕ\restriction_H)+h_{top}(\barϕ)\,,$$ where $\barϕ:G/H\to G/H$ is the map induced by $ϕ$. We concentrate on the case when $G$ is locally compact totally disconnected and $H$ is either compact or normal. Under these hypotheses, we show that the above additivity property holds true whenever $ϕH=H$ and $\ker(ϕ)\leq H$. As an application we give a dynamical interpretation of…