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1999 Summer Conference on Topology and its Applications
August 4-7, 1999
C.W. Post Campus of Long Island University
Brookville, NY, USA

Organizers
Sheldon Rothman, Ralph Kopperman

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On a Smyth Conjecture
by
Michael A. Bukatin
Brandeis University
Coauthors: Svetlana Yu. Shorina (Moscow State University)

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 I 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.

Date received: March 26, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-06.