Almost periodic points and minimal sets in topological spaces

Chikara Fujita; Hisao Kato

doi:10.4995/agt.2009.1737

Authors

Chikara Fujita University of Tsukuba
Hisao Kato University of Tsukuba

DOI:

https://doi.org/10.4995/agt.2009.1737

Keywords:

Almost periodic points, Minimal sets, w-regular space.

Abstract

In the paper [Almost periodic points and minimal sets in w-regular spaces, Topology Appl. 154 (2007), 2873–2879], Mai and Sun showed that several known results concerning almost periodic points and minimal sets of maps can be generalized from regular spaces to w-regular spaces. Also, they have three unsolved problems. In this paper, we answer to all problems which remain unsolved in the paper of Mai and Sun. In fact we prove some general theorems which give counte rexamples of the problems.

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Author Biographies

Chikara Fujita, University of Tsukuba

Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan.

Hisao Kato, University of Tsukuba

Institute of Mathematics, University of Tsukuba, Ibaraki, 305-8571 Japan.

References

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J.-H. Mai and W.-H. Sun, Almost periodic points and minimal sets in !-regular spaces, Topology Appl. 154 (2007), 2873–2879. http://dx.doi.org/10.1016/j.topol.2007.06.007

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