On stronger and weaker forms of continuity in GTS – properties and dynamics

In the first parts of this paper we consider relationships between some aspects of continuity in generalized topological (metric) spaces. The last part is devoted to the dynamics of Darboux and quasi-continuous functions. The obtained results allow to answer the important questions connected with on...

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Bibliographic Details
Published in:Topology and its applications 2016-03, Vol.201, p.274-290
Main Authors: Pawlak, Ryszard J., Korczak-Kubiak, Ewa, Loranty, Anna
Format: Article
Language:English
Subjects:
(Perfectly) transitive function
(Strongly, quasi) continuous function
Almost natural metric
Base of GMS
Blumberg set
Cliquish function
Darboux function
Devaney's chaos
Generalized topological (metric) space
Natural generalized topology
Orbit
Oscillation of function
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Summary:In the first parts of this paper we consider relationships between some aspects of continuity in generalized topological (metric) spaces. The last part is devoted to the dynamics of Darboux and quasi-continuous functions. The obtained results allow to answer the important questions connected with one dimensional dynamical systems.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2015.12.041