It is the problem to be solved that how to combine topology homeomorphic of urban planning with.

The ACL Property of Homeomorphisms under Weak Conditions;

Some existence and uniquencess results are obtained for the nonlinear fourth order elliptic boundary value problems by using some results about the global homeomorphism theory and dynamical system theory respectively.

By using homeomorphism method and the extended inverse function theorem,the existence and uniqueness of the solution for the semi-linear pseudoparabolic equations is obtained.

In this paper,the author researches the sufficient conditions which make the compact orientable submainfolds of the unit sphere homeomorphic to the sphere.

The main results are by Anderson that are l~2 is homeomorphic to R~∞, and T×Q is homeomorphic to Q ,where Q is the Hilbert cube ,T is the subspase ([0,1]×{0})×({1/2}×[0,1]) of [0,1]×[0,1], which looks like the letter l~2 and R~∞are not homeomorphism ,but it is true for the infinite-dimensional space R~∞? Frech arised the question that whether l.

In this paper,we discuss smoothly conjugating equivalence of some local diffeomorphisms with hy- perbolic fixed points on finite dimensional space.

In the paper several counterexamples of diffeomorphism used in analysis are constructed.

We mainly discuss that diffeomorphism can keep Poisson structure on Poisson manifold.

It is proved that if a homeomorphism f on a compact metric space with the POTP is distal homeomorphism, then f does not have the average shadowing property.