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International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 273-277
http://dx.doi.org/10.1155/S0161171292000358

Derived length for arbitrary topological spaces

School of Mathematics and Computer/Information Sciences, University of Hyderabad, Central University P.O., Hyderabad 500 134, India

Received 8 February 1988; Revised 15 February 1989

Copyright © 1992 Hindawi Publishing Corporation. 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

The notion of derived length is as old as that of ordinal numbers itself. It is also known as the Cantor-Bendixon length. It is defined only for dispersed (that is scattered) spaces. In this paper this notion has been extended in a natural way for all topological spaces such that all its pleasing properties are retained. In this process we solve a problem posed by V. Kannan. ([1] Page 158).