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- Neighbourhood/Neighborhood
- A neighbourhood of a point x is a set containing an open set which in turn contains the point x. More generally, a neighbourhood of a set S is a set containing an open set which in turn contains the set S. A neighbourhood of a point x is thus a neighbourhood of the singleton set {x}. (Note that under this definition, the neighbourhood itself need not be open. Many authors require that neighbourhoods be open; be careful to note conventions.)
- Neighbourhood base/basis
- See Local base.
- Neighbourhood system for a point x
- A neighbourhood system at a point x in a space is the collection of all neighbourhoods of x.
- Net
- A net in a space X is a map from a directed set A to X. A net from A to X is usually denoted (xα), where α is an index variable ranging over A. Every sequence is a net, taking A to be the directed set of natural numbers with the usual ordering.
- Normal
- A space is normal if any two disjoint closed sets have disjoint neighbourhoods. Every normal space admits a partition of unity.
- Normal Hausdorff
- A normal Hausdorff space (or T4 space) is a normal T1 space. (A normal space is Hausdorff if and only if it is T1, so the terminology is consistent.) Every normal Hausdorff space is Tychonoff.
- Nowhere dense
- A nowhere dense set is a set whose closure has empty interior.
Read more about this topic: Glossary Of Topology