Symmetric g Functions
by
Abdul Mohamad
University of Auckland
Coauthors: Chris Good

A g function on a space X with topology \tau is a mapping g: \omega×X --> \tau such that: x in g(n, x) for all n in \omega and g(n+1, x) subset g(n, x). A number of generalized metrizability properties can be characterized (or are indeed defined) in terms of g functions. In this talk we look at symmetric g functions in the following sense: A g function g is said to be symmetric if, for any n in \omega and x and y in X, y in g(n, x) whenever x in g(n, y). Using symmetric g functions, we will sort generalized metric spaces into several classes.

Date received: April 30, 2002