In this paper, the concepts of the strong accumulation point and the derived set in L-fuzzy topological spaces are introduced and their properties are systematically discussed.

It is proved that there are countable infinite discontinuous points in plane bounded closed region D, and these discontinuous points in D only have not many of accumulation points bounded functions which are also integrable functions on D.

Through comparing the different topological structures in real number space the author,finds some relatives among many topological structures in real number space and draws related properties of accumulation point and limit point in different topological structures.

By changing the perturbution to strongly monotone VIP,basing on the equivalent D-gap function,a derivative-free algorithm is given,and each accumulation point obtained by this algorithm is a solution to the original VIP under suitable conditions.

We investigate the asymptotic spectrum and accumulation of transport operator A in slab geometry with continuous energy, anisotropic scattering and inhomogeneous medium,under generalized boundary conditions.

In Lp(1 ≤p <±∞) space we show the relative compactness of the operator K = A - B , obtain the new results of asymptotic point spectrum and accumulation of operator A .