In topology and related areas of mathematics, the neighbourhood system or neighbourhood filter for a point x is the collection of all neighbourhoods for the point x.
A neighbourhood basis or local basis for a point x is a filter base of the neighbourhood filter, i.e. a subset
such that
- .
That is, for any neighbourhood we can find a neighbourhood in the neighbourhood basis which is contained in .
Conversely, as with any filter base, the local basis allows to get back the corresponding neighbourhood filter as .
Read more about Neighbourhood System: Examples, Properties
Famous quotes containing the word system:
“As long as learning is connected with earning, as long as certain jobs can only be reached through exams, so long must we take this examination system seriously. If another ladder to employment was contrived, much so-called education would disappear, and no one would be a penny the stupider.”
—E.M. (Edward Morgan)