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Definition of Open set
1. Noun. (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. ¹
2. Noun. (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. ¹
3. Noun. (topology) Most generally, a member of the topology of a given topological space. ¹
¹ Source: wiktionary.com
Lexicographical Neighbors of Open Set
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