{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/18036"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/18036","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"The theory and some applications of Pták's method of non-discrete mathematical induction","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. 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Throughout the exposition the editorial \"we\" is to be understood in the sense of Halmos [ 18]; \"we\" means \"the author and the reader\"."]},{"key":"dc:title","label":"Title","values":["The theory and some applications of Pták's method of non-discrete mathematical induction"]}]}],"canonical_facts":{"dc:contributor.advisor":["Webb, John H"],"dc:creator":["Marsh, Terence Anthony"],"dc:date.accessioned":["2016-03-21T19:06:02Z"],"dc:date.available":["2016-03-21T19:06:02Z"],"dc:date.issued":["1977"],"dc:description":["Bibliography: p. 79-80."],"dc:description.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. 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