Titlebook: Basic Concepts of Algebraic Topology; Fred H. Croom Textbook 1978 Springer-Verlag New York 1978 Algebra.Basic.Derivation.Manifold.Morphism

erythema

Duplex Unwinding with DEAD-Box Proteins, that two closed paths in a space are homotopic provided that each of them can be “continuously deformed into the other.” In Figure 4.1, for example, paths . and . are homotopic to each other and . is homotopic to a constant path. Path . is not homotopic to either . or . since neither . nor . can be pulled across the hole that they enclose.

飛鏢

有雜色

,Chain Statistics — Helical Wormlike Chains,Topology is an abstraction of geometry; it deals with sets having a structure which permits the definition of continuity for functions and a concept of “closeness” of points and sets. This structure, called the “topology” on the set, was originally determined from the properties of open sets in Euclidean spaces, particularly the Euclidean plane.

conquer

Relinquish

Single-Molecule Studies of RecBCD,This chapter is designed to show the power of the fundamental group. We shall consider a class of mappings ., called “covering projections,” from a “covering space” . to a “base space” . to which we can extend the Covering Homotopy Property discussed in Chapter 4. Precise definitions are given in the next section.

CRUDE

Geometric Complexes and Polyhedra,Topology is an abstraction of geometry; it deals with sets having a structure which permits the definition of continuity for functions and a concept of “closeness” of points and sets. This structure, called the “topology” on the set, was originally determined from the properties of open sets in Euclidean spaces, particularly the Euclidean plane.

fringe

Simplicial Homology Groups,Having defined polyhedron, complex, and orientation for complexes in the preceding chapter, we are now ready for the precise definition of the homology groups. Intuitively speaking, the homology groups of a complex describe the arrangement of the simplexes in the complex thereby telling us about the “holes” in the associated polyhedron.

出來

Covering Spaces,This chapter is designed to show the power of the fundamental group. We shall consider a class of mappings ., called “covering projections,” from a “covering space” . to a “base space” . to which we can extend the Covering Homotopy Property discussed in Chapter 4. Precise definitions are given in the next section.

Oration

https://doi.org/10.1007/978-1-4684-9475-4Algebra; Basic; Derivation; Manifold; Morphism; Topology; theorem

Grasping

Springer-Verlag New York 1978