Theorems on the representability of spaces as unions of at most countably many homogeneous subspaces

A topological space $X$ is said to be homogeneous if for any $x, y\in X$ there exists a self-homeomorphism $f$ of $X$ such that $f(x)=y$.
We propose a method for constructing topological spaces representable as a union of $n$ but not fewer homogeneous subspaces, where $n$ is an arbitrary given positive integer. Further, we present a solution of a similar problem for the case of infinitely many summands.