International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1987 / Article

Open Access

Volume 10 |Article ID 316431 | https://doi.org/10.1155/S0161171287000279

D. C. Kent, Reino Vainio, "Order compatibility for Cauchy spaces and convergence spaces", International Journal of Mathematics and Mathematical Sciences, vol. 10, Article ID 316431, 8 pages, 1987. https://doi.org/10.1155/S0161171287000279

Order compatibility for Cauchy spaces and convergence spaces

Received28 Jul 1986

Abstract

A Cauchy structure and a preorder on the same set are said to be compatible if both arise from the same quasi-uniform convergence structure on X. Howover, there are two natural ways to derive the former structures from the latter, leading to “strong” and “weak” notions of order compatibility for Cauchy spaces. These in turn lead to characterizations of strong and weak order compatibility for convergence spaces.

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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