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On the Structure of Acyclic Binary Relations Read chapter Read first chapter

2018 | OriginalPaper | Chapter

Topological MI-Groups: Initial Study

Authors : Michal Holčapek, Nicole Škorupová

Published in: Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications

Publisher: Springer International Publishing

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Abstract

In this paper, we introduce the concept of topological MI-groups, where the MI-group structure, which naturally generalizes the group structure, is enriched by a topology and the respective binary operation and inversion are continuous. To demonstrate that the proposed generalization of topological groups is meaningful, we prove that there are the products of topological MI-groups and the topological quotient MI-groups. The concept of topological MI-group is demonstrated on examples.

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Footnotes
1
It should be noted that Markov called this novel structure as quasimodule, which is, however, terminologically confusing with the standard denotation, since no scalar operation is consider here.
 
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Metadata
Title
Topological MI-Groups: Initial Study
Authors
Michal Holčapek
Nicole Škorupová
Copyright Year
2018
Book
Information Processing and Management of Uncertainty in Knowledge-Based Systems. Applications

Print ISBN: 978-3-319-91478-7

Electronic ISBN: 978-3-319-91479-4

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91479-4_50

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