Chapter 67 - Some problems from George Mason University

Abstract

This chapter discusses some of Kulesza's problems, Levy's problems, and Matveev's problems raised at George Mason university. The behavior of dimension for nonseparable metric spaces is not well understood, despite having been studied for well over half a century; there are no analogs for several important theorems regarding dimension in separable spaces and generally the results and examples are quite complicated. Almost any new theorem or example relating to the covering dimension dim would be interesting; there are several problems in the chapter that are of interest. The focus is on two fundamental problems that remain largely unsolved. The relatively recent remarkable example νμ0 of Mrówka gives a consistent solution to one of the great problems in dimension theory. Its finite powers give examples of metric spaces for which dim-ind, the discrepancy between covering and the small inductive dimension, can be any positive integer. The chapter elaborates problems in dimension theory of nonseparable metric spaces. A question about weak P-points is also discussed in the chapter.