WEDNESDAY, AUGUST 26: Ittay Weiss, University of the South Pacific, will discuss "Weak fibrations
and a metric formalism for topology". At CCNY; tea 3:15pm, talk 4pm, NAC 4/205. For more information, contact Ralph
ABSTRACT: Continuity spaces give rise to a category of (generalized) metric space which is equivalent to the category of topological spaces. Classical topological spaces and continuity spaces are thus different models of the same thing, and which models are better depends on the question at hand. I will present a simple machinery cast in the language of fibrations, resulting in a mechanism that converts metric constructions into topological ones, or into uniform ones. Two main special cases recover (in the uniform case) and generalize (in the topological case) recent work on discrete homology and discrete homotopy of metric spaces.
THURSDAY, OCTOBER 15: Michael Mislove, Department of Computer Science, Tulane University, will
speak on "From Haar to Lebesgue via Domain Theory". At Queensboro Community College, Science Building; tea 12:30-1 pm,
Room 231, talk 1-2 pm, Room 212. For more information, contact Francis Jordan,
ABSTRACT: This talk starts with the almost classic result of SchmidtÕs that the canonical map from the middle-third Cantor set to the unit interval maps Haar measure to Lebesgue measure. The Haar measure in question is defined by viewing the Cantor set as an infinite product of two-point groups. We show that there is a broad generalization of this result:
Theorem: Any compact, perfect, totally disconnected metric group admits a mapping onto the unit interval that sends Haar measure to Lebesgue measure.
The Haar measure here can be taken to be the unique left-invariant probability measure that such a group possesses. We use the lexicographic order on such a group, realized as a subset of an infinite product of finite groups, to describe how the mapping from the group to the unit interval gives a representation of real numbers in [0,1] in the group. This is joint work with Will Brian.
For more information, contact:
CCNY: R. Kopperman (845-915-0914), S. Popvassilev (646-257-7197)
College of Staten Island (718-982-3626): P. R. Misra
Baruch College (646-312-4136): A. Todd
LIU C. W. Post Center (516-299-2447): S. Andima
Medgar Evers College, (718-270-6416): H. Pajoohesh
Queensborough Community College, (718-281-5291): F. Jordan