Mathematics Colloquium

Thursday, March 23

Time: 3:35 p.m. — 4:35 p.m.

Location: Science Center Room 323

Tags:  Arts and Sciences, Colloquia, Mathematics, Sciences

Cost:  Free

Speaker: Nick Harner

Advisor: Dr. Joe Mashburn

Title: Some Implications of Neighborhood Homogeneity

Abstract: A space X is called neighborhood homogeneous if for any points a and b of X, there exist neighborhoods U and V of and a homeomorphism f such that  f(U)=V and f(p)=q. First we will observe that in zero dimensional Hausdorff spaces, neighborhood homogeneity implies homogeneity. We then utilize that proof to generalize a construction from J. van Mill which decomposed R into disjoint homogeneous homeomorphic subsets. We will also provide an example of a space which is neighborhood homogeneous but not homogeneous as well illustrate the difficulties arise for applying neighborhood homogeneity to non-zero dimensional spaces.Refreshments are available at 3:00 PM in SC 313F.

The department colloquia are held every Thursday (excluding holidays) at 3:35 pm in room SC 323 unless otherwise noted. All are invited to attend. 

Contact Information:

Name:  Paul Eloe
Email:  peloe1@udayton.edu