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

Master Thesis

1977

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http://hdl.handle.net/11427/18036
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thesis_sci_1977_marsh_terence_anthony.pdf (1.4 MB)
Authors
Marsh, Terence Anthony
Supervisors
Webb, John H
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University of Cape Town

Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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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".
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Bibliography: p. 79-80.

Keywords
Mathematics

Reference:

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

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