Approach Theory in Merotopic, Cauchy and Convergence Spaces. II |
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| Authors: | R Lowen Yoon Jin Lee |
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| Institution: | (1) R.U.C.A. Department of Mathematics and Computer Science, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium;(2) Department of Mathematics, Yonsei University, Seoul, Korea, 120-749 |
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| Abstract: | We define the notions of approach-Cauchy structure and ultra approach-Cauchy structure. We study the categorical properties of ACHY and uACHY and show that in these schemes Cauchy spaces and extended pseudo-(ultra)metric spaces are regarded as entities of the same kind. Furthermore, we investigate the relation with convergence-approach spaces and obtain a relationship similar to that of CONV and CHY. |
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