The theory and some applications of Pták's method of non-discrete mathematical induction

• Main Author: Marsh, Terence Anthony
• Other Authors: Webb, John H
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2016
• Subjects: Mathematics
• Online Access: http://hdl.handle.net/11427/18036

Bibliography: p. 79-80. === 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".