Genericity of infinite entropy for maps with low regularity

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy always finite. manifolds dimension two or greater, we show that in the closure space homeomor- phisms, with respect to either H older or Sobolev topologies, entropy generically infinite. We also prove versions C1-Closing Lemma in these spaces. Finally, give examples infinite which are and/or every exponent.