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Functions with closed graphs.

University of British Columbia

This paper concerns itself mainly with those functions from one topological or metric space to another that have closed graphs in the product space. Their relationship to closed, locally closed, compact, continuous and subcontinuous functions is studied in order to determine the relative strength of the closed graph condition. The paper collects and in some cases extends results found in papers by R. V. Fuller [2], P. E. Long [7] P. Kostyrko and T. Shalat [4], [5] and [6]. The main theorems deal with; 1) the characterization of continuous functions in terms of subcontinuity and the closed graph property; 2) a proof that if f has a closed graph then f is the limit of a sequence of continuous functions; and 3) a study of the operations under which the class of functions with closed graphs is closed.

Text

2011-06-14

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http://hdl.handle.net/2429/35407

Mathematics

University of British Columbia

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