10 citations · 42 across the 12 of their papers we have counts for
12 papers
Long colimits of topological groups IV: Spaces with socks
Rafael Dahmen, Gábor Lukács
The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact sup…
Long colimits of topological groups III: Homeomorphisms of products and coproducts
Rafael Dahmen, Gábor Lukács
The group of compactly supported homeomorphisms on a Tychonoff space can be topologized in a number of ways, including as a colimit of homeomorphism groups with a given compact sup…
Long colimits of topological groups II: Free groups and vector spaces
Rafael Dahmen, Gábor Lukács
Topological properties of the free topological group and the free abelian topological group on a space have been thoroughly studied since the 1940s. In this paper, we study the fre…
Long colimits of topological groups I: Continuous maps and homeomorphisms
Rafael Dahmen, Gábor Lukács
The union of a directed family of topological groups can be equipped with two noteworthy topologies: the finest topology making each injection continuous, and the finest group topo…
On the quasi-component of pseudocompact abelian groups
D. Dikranjan, Gábor Lukács
In this paper, we describe the relationship between the quasi-component q(G) of a (perfectly) minimal pseudocompact abelian group G and the quasi-component q(\widetilde G) of its c…
Compact-like abelian groups without non-trivial quasi-convex null sequences
D. Dikranjan, Gábor Lukács
In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We chara…
On zero-dimensionality and the connected component of locally pseudocompact groups
Dikran Dikranjan, Gábor Lukács
A topological group is locally pseudocompact if it contains a non-empty open set with pseudocompact closure. In this note, we prove that if G is a group with the property that ever…
Locally precompact groups: (Local) realcompactness and connectedness
W. W. Comfort, G. Lukács
A theorem of A. Weil asserts that a topological group embeds as a (dense) subgroup of a locally compact group if and only if it contains a non-empty precompact open set; such group…
Locally compact abelian groups admitting non-trivial quasi-convex null sequences
Dikran Dikranjan, Gábor Lukács
In this paper, we show that for every locally compact abelian group G, the following statements are equivalent: (i) G contains no sequence {x_n} such that {0} \cup {\pm x_n : n \in…
Quasi-convex sequences in the circle and the 3-adic integers
Dikran Dikranjan, Gábor Lukács
In this paper, we present families of quasi-convex sequences converging to zero in the circle group T, and the group J_3 of 3-adic integers. These sequences are determined by an in…
Lifted closure operators
Gábor Lukács
In this paper, we study the properties of closure operators obtained as initial lifts along a reflector, and compactness with respect to them in particular. Applications in the are…
Hereditarily h-complete groups
Gábor Lukács
A topological group G is h-complete if every continuous homomorphic image of G is (Raikov-)complete; we say that G is hereditarily h-complete if every closed subgroup of G is h-com…