The theory and some applications of Pták's method of non-discrete mathematical induction
Master Thesis
1977
Permanent link to this Item
Authors
Supervisors
Journal Title
Link to Journal
Journal ISSN
Volume Title
Publisher
Publisher
University of Cape Town
Faculty
License
Series
Abstract
The aim of this thesis is three-fold: (1) to develop the theory of small functions; (2) to synthesize Pták's work presented in his papers [10], [11], ..., [16] into a coherent body of knowledge; (3) to elaborate on Pták's work (i) by providing small function generalizations of Banach's Fixed Point Theorem and Edelstein's Extended Contraction Principle; (ii) by connecting the Induction Theorem to Baire's Category Theorem and Cantor's Intersection Theorem. Throughout the exposition the editorial "we" is to be understood in the sense of Halmos [ 18]; "we" means "the author and the reader".
Description
Bibliography: p. 79-80.
Keywords
Reference:
Marsh, T. 1977. The theory and some applications of Pták's method of non-discrete mathematical induction. University of Cape Town.