Compatible Group Topologies

Locally Quasi-Convex Compatible Topologies on a Topological Group

For a locally quasi-convex topological abelian group (G, τ), we study the poset C (G, τ) of all locally quasi-convex topologies on G that are compatible with τ (i.e., have the same dual as (G, τ)) ordered by inclusion. Obviously, this poset has always a bottom element, namely the weak topology σ(G, Ĝ). Whether it has also a top element is an open question. We study both quantitative aspects of ...

Compatible topologies and bornologies on modules

Compatible topologies and bornologies on modules are introduced and studied.

Compact Group Topologies for R

There is a compact solenoidal group S that is group isomorphic to the additive real numbers R. The existence of 5 leads to a study of compact real groups; that is, compact groups which are group isomorphic to R. The compact real groups are characterized as products of 5. Various conditions on a topological group G are given which are equivalent to G being compact real. It is shown that any comp...

Compact compatible topologies for graphs with small cycles

A topology τ on the vertices of a comparability graph G is said to be compatible with G if each subgraph H of G is graph-connected if and only if it is a connected subspace of (G,τ). In two previous papers we considered the problem of finding compatible topologies for a given comparability graph and we proved that the nonexistence of infinite paths was a necessary and sufficient condition for t...

Order-compatible Topologies on a Partially Ordered Set