182 research outputs found
Topo-Groups and a Tychonoff Type Theorem
In this article, we introduce an interesting topology-like concept concerning
groups (and with almost the same method it can be defined for other algebraic
systems). Given an arbitrary group , we define a {\em topo-system} on as
a set of subgroups satisfying certain conditions like a topology on a set. We
will call such a group, a {\em topo-group}. These topo-groups are not rare and
as we will see, there are many examples of topo-groups. We investigate
fundamental notions concerning topo-groups and we see that many basic concepts
of topology can be introduced in the frame of topo-groups. A {\em filter of
subgroups} will be defined in such way that we will be able to formulate a
Tychonoff type theorem for the direct product of {\em topo-compact}
topo-groups.Comment: 9 pages, Revise
Existentially closed structures and some embedding theorems
Using the notion of existentially closed structures, we obtain embedding
theorems for groups and Lie algebras. We also prove the existence of some
groups and Lie algebras with prescribed properties.Comment: 14 pages, 2 new sections are added, some corrections mad
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