An example concerning inverse limit sequences of normal spaces

Abstract

Using techniques developed by Wage and Przymusiński, we construct an inverse limit sequence ( X n , f n m ) ({X_n},{f_{nm}}) with limit space X such that each X n {X_n} is Lindolöf with dim ⁡ X n = 0 \dim {X_n} = 0 , where dim denotes covering dimension, while X is normal with dim ⁡ X > 0 \dim X > 0 . The space X is a counterexample to several conjectures in Topology.