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Topology

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Examples of Hausdorff Spaces I

TOPO-MTJZLE

Which of the following topological spaces is NOT a Hausdorff space?

A

$\mathbb{R}$ with the standard (metric) topology.

B

The Euclidean plane $\mathbb{R}^2$ with the standard (metric) topology.

C

$\mathbb{R}$ with the discrete topology.

D

$\mathbb{R}$ with the trivial topology $\{\emptyset, \mathbb{R}\}$

E

The unit interval $[0,1]$ with the topology given by the usual Euclidean metric on $\mathbb{R}$ restricted to $[0,1]$.