Band of topological groups
Sunil Kumar Maity, Monika Paul

TL;DR
This paper explores the structure of bands of topological groups derived from cryptogroups, establishing conditions for metrizability and Hausdorff properties related to normal subcryptogroups.
Contribution
It introduces the concept of a band of topological groups from cryptogroups and characterizes their metrizability and quotient space properties.
Findings
A band of topological groups is metrizable iff each $\
6$-class is metrizable.
The quotient $S/N$ is Hausdorff iff $ ho_{_N}$ is closed in $S imes S$.
Abstract
In this article, we construct a band of topological groups from a cryptogroup. Also, we prove that a band of topological groups is metrizable if and only if each -class is metrizable. Finally, we demonstrate that if is a band of topological groups and is a full normal subcryptogroup of , then is Hausdorff if and only if is closed in if and, is closed in if and only if is closed in .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Logic · Mathematics and Applications · Geometric and Algebraic Topology
