Towards a theory of representations
Many mathematicians familiar with the constructivistic objections to classical mathematics concede their validity but remain unconvinced that there is a satisfactory alternative. In this paper we present representations as a foundation for a theory of constructivity in mathematics. Computability and continuity w.r.t. given representations are defined and studied in connection witth reducibility. We investigate topological properties of representations and introduce (continuously-) admissible representations of seperable T₀-spaces. It is shown that the continuity theory induced by (continuously-) admissible representations corresponds to the topological continuity theory. Hence these representations are very appreciate to study construtivity on all kinds of seperable T₀-spaces.
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