Talk:Discrete space
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Boundedness[edit]
- "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)
- "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)
A finite space is Hausdorff iff it is discrete[edit]
Should this be included in "properties"? Nikolaih☎️📖 21:22, 27 May 2021 (UTC)