Topology Proceedings
Document # baak-09
Electronic Version 24 Summer (1999) |
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On a Smyth Conjecture
Michael A. Bukatin and Svetlana Yu. Shorina
The set Ix = {y \in A | {x,y} is unbounded} is an observable continuous representation of negative information about x \in A for a weakly Hausdorff continuous dcpo A with the Scott topology. When A is not weakly Hausdorff the largest continuous approximation of Ix is represented by Jx = {y \in A | x \in Int(Iy)}, and the largest observable continuous representation of Ix is represented by J'x = Int(Jx). Mike Smyth conjectured, that J or J' is closely related to the least symmetric closed tolerance on A. In this paper we establish that, indeed, {<x, y >| y \in J'x} is the complement of this tolerance.
We also establish a relationship between this tolerance and lower bounds of relaxed metrics on A.
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Copyright © 2001
Nipissing University
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Date published electronically: March 5, 2001.