Year: 2013
Type: preprint
Abstract: 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 $G$, we define a {\em topo-system} on $G$ 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.
Source: arXiv (Cornell University)
Author: Shahryari, M.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1538680759