The Notion of Homotopy

I. M. James
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I. M. James: Oxford University, Mathematical Institute

Chapter Chapter 5 in General Topology and Homotopy Theory, 1984, pp 137-166 from Springer

Abstract: Abstract In this chapter we study the classification of maps by homotopy or continuous deformation. The subject is best approached by first considering a special case. Recall that a path in a space X is simply a map λ: I → X. The parameter t ∈ I is usually thought of as a measure of time, so that as t runs from 0 to 1 the image point λ(t) runs from λ(0) to λ(1). When λ(0) = λ(1) = x, say, the path λ is called a loop, specifically a loop based at x.

Keywords: Homotopy Class; Homotopy Type; Smash Product; Homotopy Equivalence; Fine Topology (search for similar items in EconPapers)
Date: 1984
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DOI: 10.1007/978-1-4613-8283-6_6

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