منابع مشابه
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 ...
متن کاملOn Mackey Topologies in Topological Abelian
Let C be a full subcategory of the category of topological abelian groups and SPC denote the full subcategory of subobjects of products of objects of C. We say that SPC has Mackey coreeections if there is a functor that assigns to each object A of SPC an object A that has the same group of characters as A and is the nest topology with that property. We show that the existence of Mackey coreeect...
متن کاملOn Mackey Topologies in Topological Abelian Groups
Let C be a class of topological abelian groups and SPC denote the full subcategory of subobjects of products of objects of C. We say that SPC has Mackey coreflections if there is a functor that assigns to each object A of SPC an object τA that has the same group of characters as A and is the finest topology with that property. We show that the existence of Mackey coreflections in SPC is equival...
متن کاملTopological Group Criterion for C(x) in Compact-open-like Topologies, I
We address questions of when (C(X), +) is a topological group in some topologies which are meets of systems of compact-open topologies from certain dense subsets of X. These topologies have arisen from the theory of epimorphisms in lattice-ordered groups (in this context called “epi-topology”). A basic necessary and sufficient condition is developed, which at least yields enough insight to prov...
متن کاملTopological group criterion for C(X) in compact-open-like topologies, II
We continue from “part I” our address of the following situation. For a Tychonoff space Y, the “second epi-topology” σ is a certain topology on C(Y), which has arisen from the theory of categorical epimorphisms in a category of lattice-ordered groups. The topology σ is always Hausdorff, and σ interacts with the point-wise addition + on C(Y) as: inversion is a homeomorphism and + is separately c...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2017
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2016.10.013