Article contents
The Nachibin quasi-uniformity of a bi-Stonian space
Published online by Cambridge University Press: 09 April 2009
Abstract
It is known that every frame is isomorphic to the generalized Gleason algebra of an essentially unique bi-Stonian space (X, σ, τ) in which σ is T0. Let (X, σ, τ) be as above. The specialization order ≤σ, of (X, σ) is τ × τ-closed. By Nachbin's Theorem there is exactly one quasi-uniformity U on X such that ∩U = ≤σ and J(U*) = τ. This quasi-uniformity is compatible with σ and is coarser than the Pervin quasi-uniformity U of (X, σ). Consequently, τ is coarser than the Skula topology of σ and coincides with the Skula topology if and only if U = P.
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 61 , Issue 3 , December 1996 , pp. 322 - 326
- Copyright
- Copyright © Australian Mathematical Society 1996
References
- 2
- Cited by