A Theory of Uniformities for Generalized Ordered Spaces

Lindgren, W. F. ; Fletcher, P.

Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 35-44

Résumé

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.

Détail

DOI : 10.4153/CJM-1979-004-4

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