A Theory of Uniformities for Generalized Ordered Spaces
| Autor: | W. F. Lindgren, P. Fletcher |
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| Rok vydání: | 1979 |
| Předmět: | |
| Zdroj: | Canadian Journal of Mathematics. 31:35-44 |
| ISSN: | 1496-4279 0008-414X |
| DOI: | 10.4153/cjm-1979-004-4 |
| Popis: | Let (X, ) be a topological space equipped with a partial order ≦ and let C (≦) denote the continuous increasing functions mapping X into R (a function f : X → R is increasing provided f(x) ≦ f(y) whenever x ≦ y) Then (X,, ≦) is an N-space (in the terminology of [16], a completely regular order space) provided is the weak topology of C (≦) and if x ≦ y is false, then there is an f ∈ C (≦) such that f(y) < f(x). L. Nachbin's introduction of N-spaces was perspicacious, for these spaces now find application in a wide spectrum of mathematics. |
| Databáze: | OpenAIRE |
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