In this paper, we define the notion of paratopological polygroups and find their topological properties. In particular, we find those properties that make a paratopological polygroup a topological polygroup. We also give an example of topological polygroup and obtain some of their properties.
The study of entropies of hypergroups in scientific disciplines such as chemistry, physics, geometry and coding theory helps us to calculate the chaos of the scientific processes of phenomena. In this respect, different entropies on hypergroups have been defined and their systemic properties have been investigated. This paper introduces the notion of hypernormed entropy on topological hypernormed hypergroups and provides some interesting examples. The study investigates the fundamental properties of this entropy such as invariance under conjugation, invariance under inversion, the logarithmic law, monotonicity for subflows and continuity for direct limits.
This paper studies topological definitions of chain recurrence and shadowing for continuous endomorphisms of topological groups generalizing the relevant concepts for metric spaces. It is proved that in this case the sets of chain recurrent points and chain transitive component of the identity are topological subgroups. Furthermore, it is obtained that some dynamical properties induced by the original system on quotient spaces.These results link an algebraic property to a dynamical property.
It is well-known that BL-algebras provide an algebraic language for logic, and play a very decisive role in the development of this theory. The present paper aims to study the entropy of a partition in a product BL-algebra. We define the entropy of a partition in an arbitrary product BL-algebra and study its properties. Finally, we investigate the effect of partition entropy on the product of BL-algebras.
2010 Mathematics Subject Classification. Primary 03G10, 03G25, 37A35, 54C70.
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