A separable metric space X is called rigid if the identity 1
X
is the only autohomeomorphism, and homogeneous if, for any points x, y of X, there is an (onto) homeomorphism h: X → X such that h(x) = y.
In this note, we show that this onto-ness of the homeomorphism h could not be removed in the definition of homogeneity, by constructing a continuum X which is rigid and has many embeddings, that is, for any two points x, y, there is an embedding (= into homeomorphism) h: X→X such that h(x) = y.