 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/ib/paper-4/10g/b/ii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Constant maps identify a copy of

S

inside

C ([0, 1], S)

. If the function space were path connected, evaluating a path of functions at

0

would give a path in

S

between any two constant values. Since

S

is not path connected,

C ([0, 1], S) is not path connected .

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