| By using the C-P structure, with respect to arbitrary subset of on general topologicalspace, a new definition of the topological pressure and the lower and upper capacitytopological pressure of a proper map are given. It does not depend on the selectionmetric, moreover do not need the space is compact. Therefore, this paper defined thetopological pressure have broader applicability. At last prove some basic properties andproviding some of the results of the multi-fractal analysis on compact spaces extensionto locally compact separable space.This paper is organized as follows:In Chapter1, we introduce the development history and the investigation status oftopological entropy and topological pressure.In Chapter2, some general conceptions, knowledge and notations are given in pre-liminaries.In Chapter3, with respect to arbitrary subset of on general topological space, anew definition of the topological pressure and the lower and upper capacity topologicalpressure of a proper map are given.In Chapter4, major research properties of the new pressure to locally compactseparable space and relationship with the PP pressure.In Chapter5, major research variational principle of new pressure in the locallycompact separable space.In Chapter6, mainly give some of the results of the multi-fractal analysis in [29] oncompact metric space extension to locally compact separable space. |
