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We prove the genericity of the shadowing and periodic shadowing propertiesfor both conservative and dissipative homeomorphisms on a compact connectedmanifold. Our proof is valid for topological manifolds and still holds in thedissipative case. As a consequence of this result, we establish the genericityof the specification property, the average shadowing property and theasymptotic average shadowing property in the conservative case.

On the genericity of the shadowing property for conservative homeomorphisms