It is a well-known fact that there are continua X such that the inverse limit of any inverse sequence $$\{X,f_n\}$$
{
X
,
f
n
}
with surjective continuous bonding functions $$f_n$$
f
n
is homeomorphic to X. The pseudoarc or any Cook continuum are examples of such continua. Recently, a large family of continua X was constructed in such a way that X is $$\frac{1}{m}$$
1
m
-rigid and the inverse limit of any inverse sequence $$\{X,f_n\}$$
{
X
,
f
n
}
with surjective continuous bonding functions $$f_n$$
f
n
is homeomorphic to X by Banič and Kac. In this paper, we construct an uncountable family of pairwise non-homeomorphic continua X such that X is 0-rigid and prove that for any sequence $$(f_n)$$
(
f
n
)
of continuous surjections on X, the inverse limit $$\varprojlim \{X,f_n\}$$
lim
←
{
X
,
f
n
}
is homeomorphic to X.
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