Talk:Hypertopology
Add topicLatest comment: 5 months ago by ~2026-10313-03 in topic A few conditions should be added, when sources can be found for them.
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A few conditions should be added, when sources can be found for them.
[edit]It should be noted that the definition of hypertopology in this article requires that X is T0; otherwise it is impossible for the canonical map to be injective.
It should also be noted that the Vietoris topology is not necessarily a hypertopology in the sense of this article if X is not T1. A counterexample for this is the pseudocircle, and this is very easy to check yourself by writing out all of the open subsets and seeing that the canonical map is not continuous. However, most research on the Vietoris topology focuses on spaces which are at least T1 and so finding a source for this fact will be hard. ~2026-10313-03 (talk) 01:33, 16 February 2026 (UTC)