## Some Cohomological aspects of the Banach Fixed Point Principle

03/03/2011 - 4:00pm
03/03/2011 - 5:00pm
Speaker:
Ludvik Janos
Abstract:

Let be a compact metrizable topological space and a continuous mapping. Let and denote the set of all compatible metrics on and the set of all continuous real valued functions on , respectively. The mapping is called a Banach contraction if for some there is some metric with for . It is known that this condition is equivalent to the statement: The “core” of , i.e., , is a singleton with . We consider the set as an abelian group on which the abelian monoid acts via for and . It turns out that the 1-co-cycle of this action is a mappring from N to defined by for , where is any function from . By the abuse of the language, we call a co-cycle and, if there exists some so that , we call a coboundary. We prove that is a Banach contraction if and only if there is a countable, point separating family of nonnegative coboundaries.

Where:
Millikan 211, Pomona College
Misc. Information:

Refreshments served at 3:45 p.m. at Harry Mullikin Room, Millikan 209

AttachmentSize
Abstract and info98.54 KB