Equicontinuity, shadowing and distality in general topological spaces

Huoyun Wang

Czechoslovak Mathematical Journal (2020)

  • Volume: 70, Issue: 3, page 711-726
  • ISSN: 0011-4642

Abstract

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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.

How to cite

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Wang, Huoyun. "Equicontinuity, shadowing and distality in general topological spaces." Czechoslovak Mathematical Journal 70.3 (2020): 711-726. <http://eudml.org/doc/297027>.

@article{Wang2020,
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.},
author = {Wang, Huoyun},
journal = {Czechoslovak Mathematical Journal},
keywords = {shadowing; chain transitive; equicontinuity; uniform space},
language = {eng},
number = {3},
pages = {711-726},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Equicontinuity, shadowing and distality in general topological spaces},
url = {http://eudml.org/doc/297027},
volume = {70},
year = {2020},
}

TY - JOUR
AU - Wang, Huoyun
TI - Equicontinuity, shadowing and distality in general topological spaces
JO - Czechoslovak Mathematical Journal
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 70
IS - 3
SP - 711
EP - 726
AB - 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.
LA - eng
KW - shadowing; chain transitive; equicontinuity; uniform space
UR - http://eudml.org/doc/297027
ER -

References

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