17 citations · 88 across the 31 of their papers we have counts for
4 papers · 1 filter
Partitions of unity and coverings
Kyle Austin, Jerzy Dydak
The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existe…
Coverings and fundamental groups: a new approach
Jerzy Dydak
The traditional approach of defining the fundamental group first and then constructing universal coverings works well only for the class of Poincar\' e spaces. For general spaces t…
Extension dimension for paracompact spaces
Jerzy Dydak
We prove existence of extension dimension for paracompact spaces. Here is the main result of the paper: \proclaim{Theorem} Suppose X is a paracompact space. There is a CW complex K…
Partitions of unity
Jerzy Dydak
The paper contains an exposition of part of topology using partitions of unity. The main idea is to create variants of the Tietze Extension Theorem and use them to derive classical…