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

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".

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1977

Author dc:creator

• Marsh, Terence Anthony

Advisor dc:contributor.advisor

• Webb, John H

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/18036

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/18036