Bauer/Logic Seminar/Nov. 16, 2000

[Margaret Jaffey]

>LOGIC SEMINAR AND COMPUTER SCIENCE SEMINAR
>
>DATE: Thursday, Nov. 16, 2000.
>TIME:  3:30-5:00
>PLACE: Ryerson (annex) 277.
>
>TITLE: Computability for Topological Spaces
>
>SPEAKER: Andrej Bauer
>          School of Computer Science
>          Carnegie Mellon University
>          Pittsburgh
>
>ABSTRACT:
>
>We will present a framework for computable topology based on recent
>developments that began in 1996 with Dana Scott's equilogical spaces.
>The starting point are two observations about the powerset of the
>natural numbers P(N), equipped with the Scott topology: first, the
>subspaces of P(N) are precisely all the countably based T_0-spaces;
>second, P(N) is equipped with a natural notion of computability,
>namely recursive enumerability. This leads to a formulation of
>computable topology on all countably based T_0-spaces, with computable
>maps between them that are defined on the non-computable as well as
>the computable points. This setup can then be extended to equilogical
>spaces by equipping the topological spaces with equivalence
>relations. The benefit of adding the equivalence relations is that
>they let us distinguish between the points of a space and the names of
>points, similar to the distinction between r.e. sets and Goedel codes
>of r.e. sets.
>
>Equilogical spaces form a category that has very good closure
>properties. For example, it is cartesian closed, which means that we
>can form all function spaces, function spaces of function spaces, etc.
>This cannot be done if we restrict attention only to topological
>spaces.  In the last part of the talk we will show how computability on
>real numbers and real functions is treated in equilogical spaces.


Visitor's Host:  Prof. Robert I. Soare




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Margaret P. Jaffey			margaret at cs.uchicago.edu
Department of Computer Science
Student Support Rep (Ry 161A)		(773) 702-6011
The University of Chicago		http://www.cs.uchicago.edu
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