Talk:Discrete space

Boundedness

"The subspace topology on the integers as a subspace of the real line is the discrete topology."

and

"Every discrete metric space is bounded."

wat — Preceding unsigned comment added by 79.227.171.159 (talk) 19:25, 4 February 2013 (UTC)[reply]

"Discrete metric space" refers to a set endowed with the discrete metric. It is a metric space concept.

On the other hand, the discrete topology is only about topology. There is no meaning of boundedness in this context. There may be different metrics that induce the discrete topology.

In other words, both the discrete metric and the Euclidean metric induce the discrete topology on the integers, but only the integers equipped with the discrete metric are a "discrete metric space". JackozeeHakkiuz (talk) 23:24, 16 April 2022 (UTC)[reply]

A finite space is Hausdorff iff it is discrete

Should this be included in "properties"? Nikolaih^☎️📖 21:22, 27 May 2021 (UTC)[reply]