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".

Reference:

Marsh, T. 1977. The theory and some applications of Pták's method of non-discrete mathematical induction. University of Cape Town.

Marsh, T. A. (1977). The theory and some applications of Pták's method of non-discrete mathematical induction. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/18036

Marsh, Terence Anthony. "The theory and some applications of Pták's method of non-discrete mathematical induction." Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1977. http://hdl.handle.net/11427/18036

Marsh TA. The theory and some applications of Pták's method of non-discrete mathematical induction. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 1977 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/18036