Mentor's Bio:

Not Available

Research Topic(s) Summary:
Algebra/Number Theory/Logic: denotational semantics
Topology: point-set topology

Description of Research:
The spaces encountered in classical analysis all have the "Hausdorff" property: each pair of distinct points lie in disjoint open sets. This is not true of spaces that I work on, which are met in computation: The computer screen, while appearing like a bounded rectangle in the plane which has an infinite number of points, really consists of only a finite number of "pixels", and since adjacent ones are often connected to each other, they cannot lie in disjoint open sets. Programs which approximate objects never attain full information (for example, a program that calculates a number, will have only a finite number of decimal places at any time). Therefore, distinct elements may appear the same up to the level known, and there will be no disjoint open sets containing them at this level.