8 papers · 1 filter
Three Problems on Separable Quotients of Precompact Abelian Groups
Li-Hong Xie, Jiang Yang
We address three problems on separable quotients of topological groups posed by Leiderman, Morris, and Tkachenko in \cite{LMT} published on Israel Journal of Mathematics. First, we…
The answer about Itzkowitz's Problems on FSIN groups
Dekui Peng, Li-Hong Xie, Jiang Yang
A topological group is functionally balanced if every bounded real-valued left uniformly continuous function is right uniformly continuous. We prove that every Hausdorff functional…
Countable uniformly discrete sets in functionally balanced groups
Dekui Peng, Li-Hong Xie, Jiang Yang
We prove that every countable left uniformly discrete subset of a Hausdorff functionally balanced topological group is right thin. As applications, we answer two questions of Bouzi…
Pseudocompact Topological \(MV\)-Algebras
Li-Hong Xie, Jiang Yang
Recently, topological MV-algebras have been investigated by several mathematicians. In this paper, we find that every topological \(MV\)-algebra is a Mal'tsev space introduced by M…
The Hartman--Mycielski construction in topological MV-algebras
Li-Hong Xie, Jiang Yang
Recently, topological MV-algebras have been investigated by several mathematicians. In this paper, we mainly show that for every Hausdorff topological MV-algebra , there exists…
Filter-induced linear topologies on residuated lattices: Hausdorffness, profiniteness, and finiteness conditions
Jiang Yang, Pengfei He, Juntao Wang
We study linear topologies on residuated lattices generated by systems of filters, with emphasis on the uniform structures and separation properties that they determine. A down-dir…
Closed Image Characterizations of Locally Finite Groups via Cellular Automata
Jiang Yang
We prove that a group is locally finite if and only if, for some (equivalently, every) infinite set , every cellular automaton has closed image in the prodiscre…
Quotient homomorphisms of Topological MV-Algebras and Applications
Li-Hong Xie, Jiang Yang
For a topological group, the quotient map modulo a subgroup is open and the quotient map modulo a compact subgroup is perfect. In this paper we prove and develop the corresponding…