open set
Noun
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Noun
open set (plural open sets)
- (topology) Informally, a set such that the target point of a movement by a small amount in any direction from any point in the set is still in the set; exemplified by a full circle without its boundary.
- (topology, analysis, restricted to metric spaces) A set which can be described as an (arbitrary) union of open balls. Equivalently, a set such that for every point in it, there is an open ball centered at that point, such that that open ball is contained by the set.
- (topology) Most generally, a member of the topology of a given topological space.
- French: ouvert, ensemble ouvert
- German: offene Menge
- Russian: откры́тое мно́жество
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.002