Let (X, d) be a compact metric space. Let T : X → X be a continuous function satisfying infn∈ℕ d(Tn(x), Tn(y)) ≠ 0 for every x, y ∈ X with x ≠ y. Then which of the following statements is true?

Question

Mathematics · Topology

Verified Solution4 Options

Answer 1

If X is finite, then T cannot be onto

Answer 2

The image of T cannot be closed in X

Answer 3

T is not a one-to-one function

Answer 4

T is a one-to-one function

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