Titlebook: Essential Topology; Martin D. Crossley Textbook 2005 Springer-Verlag London Limited 2005 Algebraic topology.Continuity.Fundamental group.H

Forsake

Topological Spaces,So far, we have only considered functions on the real line. We have seen how to hide those annoying ?s and δs in the definition of continuity, replacing them with open sets. This enables us to consider functions with domains and ranges different from R; all we need is some notion of “open set”.

stress-response

tolerance

Homotopy Groups,In Chapter 6 we calculated the set [S., S.] of homotopy classes of maps S1 → S1 and found that [S., S.] = Z, which is an Abelian group. We can describe the group operation topologically as follows.

Legend

More Deconstructionism,In Chapter 5, we studied the union, product and quotient constructions. These are elementary constructions, in the sense that they involve constructing a topological space directly. In this chapter, we will look at some non-elementary constructions which are built out of these elementary ones.

小歌劇

Abnormal

institute

Homotopy,ibe all the continuous maps between any given pair of topological spaces. Of course, with almost any pair of spaces, there are lots of continuous functions between them – far more than we can ever hope to list or understand. For example, it is not remotely feasible to list even the continuous functi

彎腰

Simplicial Homology,ace. However, homotopy groups are very hard to calculate. In this chapter we introduce “homology” groups, which can be thought of as a rough approximation to the homotopy groups of a space. In defining the homotopy groups of a space X, we considered all maps

Amenable

lactic

The Homicidal Patientiatrists can reach reliable and valid conclusions concerning these questions, which have awesome implications for the lives of the patients being evaluated, such as: Should they be free persons? Should they be involuntarily held? Should they be tried for offenses and perhaps sent to prison?