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- Sep 29th 2009, 07:14 AM #1

- Joined
- Sep 2009
- Posts
- 21

## New Question

A subset A of a metric space X is called uniformly discrete if there

epsilon> 0 with the property that the distance between two distinct points of A is always

greater or equal to epsilon:

∀ a, b ∈ A, (a!= b) ⇒ (dX (a, b) ≥ epsilon).

Show that any subset of a uniformly discrete metric space X is

closed in X.

- Sep 29th 2009, 07:33 AM #2

- Sep 30th 2009, 10:41 AM #3