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.