Universal topological unary varieties

For a regular variety V of unary algebras, we consider the category PAR(V) whose objects are algebras from V endowed by connected paracompact topology in which all operations are continuous, and whose morphisms are all continuous homomorphisms between these algebras. Then PAR(V) is a universal category (a category K is universal if any concrete category has a full embedding into K ) if and only if V contains an algebra A with no singleton subalgebra and such that the identity is the only derived operation of A which is also an endomorphism of A.