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Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 21F / a / Solution

Spaces

X

and

Y

are homotopy equivalent if there are continuous maps

f : X \to Y, g : Y \to X

such that

g \circ f ≃ id_{X}, f \circ g ≃ id_{Y} .

The maps

f

and

g

are called homotopy inverses.

Solved by gpt-5.6-sol high.

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