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Czechoslovak Mathematical Journal, Vol. 70, No. 3, pp. 711-726, 2020

Equicontinuity, shadowing and distality in general topological spaces

Huoyun Wang

Received November 4, 2018.   Published online January 16, 2020.
Abstract:  We consider the notions of equicontinuity point, sensitivity point and so on from a topological point of view. Many of these notions can be sensibly defined either in terms of (finite) open covers or uniformities. We show that for the notions of equicontinuity point and sensitivity point, Hausdorff or uniform versions coincide in compact Hausdorff spaces and are equivalent to the standard definitions stated in terms of a metric in compact metric spaces. We prove that a uniformly chain transitive map with uniform shadowing property on a compact Hausdorff uniform space is either uniformly equicontinuous or it has no uniform equicontinuity points.
Keywords:  shadowing; chain transitive; equicontinuity; uniform space
Classification MSC:  37B20, 37B05, 54H20
DOI:  10.21136/CMJ.2020.0488-18
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Affiliations:   Huoyun Wang, Department of Mathematics of Guangzhou University, 230 Wai Huan Xi Road, Guangzhou Higher Education Mega Center, Guangzhou 510006, P. R. China, e-mail: wanghuoyun@126.com
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