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Journal of Function Spaces and Applications
Volume 2013, Article ID 275702, 3 pages
http://dx.doi.org/10.1155/2013/275702
Research Article

The Space of Continuous Periodic Functions Is a Set of First Category in

1College of Mathematics and Information Science, Jiangxi Normal University, Nanchang, Jiangxi 330022, China
2Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA

Received 17 January 2013; Accepted 12 February 2013

Academic Editor: Józef Banaś

Copyright © 2013 Zhe-Ming Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We prove that the space of continuous periodic functions is a set of first category in the space of almost periodic functions, and we also show that the space of almost periodic functions is a set of first category in the space of almost automorphic functions.