Titlebook: General Topology and Homotopy Theory; I. M. James Textbook 1984 Springer-Verlag New York Inc. 1984 Homotopy.cofibration.fibrations.group t

Encapsulate

RALES

灾祸

Introduction,basic category of topological spaces and continuous functions but also with various other categories associated with it. Consequently we begin with a preliminary chapter in which some of the common features of these categories are discussed in general terms. This avoids a certain amount of repetitio

elastic

The Basic Framework,to some extent. At the very least it saves a certain amount of repetition. In fact all the categories we shall be dealing with are of the type known as concrete, i.e. they consist of sets with additional structure and functions which respect that structure. However there is little to be gained by re

反叛者

The Axioms of Topology,s hardly anything which cannot be found in the standard texts. However by selecting only the relevant material and omitting everything else I believe it is possible to give a clearer picture of this part of the subject, at least from the point of view I have adopted.

MILL

Spaces Under and Spaces Over,sociated with the category T of spaces and maps. We begin by discussing the category of spaces under a given space, then turn to the category of spaces over a given space, and finally consider the category of spaces over and under a given space.

Alpha-Cells

The Notion of Homotopy,al case. Recall that a path in a space . is simply a map .: . → . The parameter . ∈ . is usually thought of as a measure of time, so that as . runs from 0 to 1 the image point .(.) runs from .(0) to .(1). When .(0) = .(1) = ., say, the path . is called a loop, specifically a loop based at .

hypnogram

Extensors and Neighbourhood Extensors,bject which is also important. In this alternative approach the main restriction is placed on the codomain of the mappings in question. In fact it is necessary to restrict the class of domains to some extent as well. For what we are going to do it will be convenient to work with paracompact domains,

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Textbook 1984nient form. In this book I have tried to take a fresh look at some of this basic material and to organize it in a coherent fashion. The text is as self-contained as I could reasonably make it and should be quite accessible to anyone who has an elementary knowledge of point-set topology and group the

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