2014年5月15日 The purpose of this book is to provide an integrated course in real and complex analysis for those who have already taken a preliminary course in real analysis. It particularly emphasises the interplay between analysis and topology. Begin
Chronology. In the year 2000 I was given two courses to teach: analysis and topology. The Analysis course was assigned to me due to an emergency redistribution; Topology was thrown in as an award for accepting to teach Analysis on such short notice.
Review I recommend the text to theoretical physicists and mathematicians who want to get exposed to a different presentation and applications of group theory. --Mathematical Reviews From the Inside Flap This book presents a survey of Topology and Di
Abstract. Given a map f : M ! N of closed topological manifolds we define torsion obstructions whose vanishing is a necessary condition for f being homotopy equivalent to a projection of a locally trivial fiber bundle. If N = S1, these torsion obstr
Algebraic Topology（Allen Hatcher） Chapter 0. Some Underlying Geometric Notions Chapter 1. The Fundamental Group Chapter 2. Homology Chapter 3. Cohomology Chapter 4. Homotopy Theory
Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy theory and type theory. It touches on topics as seemingly dis
The first purpose of this paper is to define a homotopy for fuzzy spaces. We continue our work by showing that the property of having a fixed point is invariant by this homotopy. These theorems generalize and improve well-known results.
Relationship between the homotopy analysis method and harmonic balance method，陈衍茂，刘济科，The relationship between the homotopy analysis method (HAM) and harmonic balance (HB) method is studied. The HAM is employed to obtain the periodic solutions of con
The evolutionary tree reconstruction algorithm called SEMPHY using structural expectation maximization (SEM) is an efficient approach but has local optimality problem. To improve SEMPHY, a new algorithm named HSEMPHY based on the homotopy continuatio
