Abstract and Applied Analysis
Volume 2008 (2008), Article ID 485706, 5 pages
Slowly Oscillating Continuity
Department of Mathematics, Faculty of Science and Letters, Maltepe University, 34857 Maltepe, Istanbul, Turkey
Received 2 November 2007; Accepted 11 February 2008
Academic Editor: Ferhan Atici
Copyright © 2008 H. Çakalli. 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.
A function is continuous if and only if, for each point in the domain, , whenever . This is equivalent to the statement that is a convergent sequence whenever is convergent. The concept of slowly oscillating continuity is defined in the sense that a function is slowly oscillating continuous if it transforms slowly oscillating sequences to slowly oscillating sequences, that is, is slowly oscillating whenever is slowly oscillating. A sequence of points in is slowly oscillating if , where denotes the integer part of . Using 's and 's, this is equivalent to the case when, for any given , there exist and such that if and . A new type compactness is also defined and some new results related to compactness are obtained.