# Slawomir Solecki: Menger compacta as projective Fraisse limits with emphasis on dimension one

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 2 December 2015, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Slawomir Solecki.

Title: Menger compacta as projective Fraisse limits with
emphasis on dimension one.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract: In each dimension d, there exists a canonical compact, second
countable space, called the d-dimensional Menger space, with certain
universality and homogeneity properties. For d = 0, it is the Cantor set,
for d = infinity, it is the Hilbert cube. I will concentrate on the
1-dimensional Menger space. I will prove that it is a quotient of
a projective Fraisse limit. I will describe how a property of projective
Fraisse limits coming from Logic, called the projective extension property,
can be used to prove high homogeneity of the 1-dimensional Menger space.