To ask whether these are homeomorphic, we need to know: what is a homeomorphism? https://en.wikipedia.org/wiki/Homeomorphism and yes, it seems to me all the Cantor sets I defined for each K>=3, including the K=3 case corresponding to Cantor's original defn, are homeomorphic. See, each point in each set is describable using a countably-infinitely-long bitstring. The Nth 0-or-1 specifies which of the two halves you went into at stage N of the construction. Simply make the bijection be: points with same bitstring correspond. Obviously it is a bijection. Then the only question is: is this bijection CONTINUOUS in both directions? It does not take long reviewing the epsilon delta defn of continuity, to claim the answer is "yes."