neighborhood

Etymology

From an alteration of earlier neighborred (“neighborhood”), from Middle English neȝeburredde, neheborreden, equivalent to neighbor + -red; the term being interpreted as neighbor + -hood. For change in suffix (-red to -hood), compare brotherhood. Cognates Dutch nabijheid (common in modern language), Dutch naburigheid (uncommon in modern language).

noun

1. The residential area near one's home.
   He lives in my neighborhood.
2. The inhabitants of a residential area.
   The fire alarmed the neighborhood.
3. A formal or informal division of a municipality or region.
   We have just moved to a pleasant neighborhood.
4. An approximate amount.
   He must be making in the neighborhood of $200,000 per year.
5. The quality of physical proximity.
   The slums and the palace were in awful neighborhood.
6. (chiefly obsolete) The quality of being a neighbor, of living nearby, next to each-other; proximity.
   Our neighborhood was our only reason to exchange hollow greetings.
   1595, George Peele, The Old Wives’ Tale, The Malone Society Reprints, 1908, lines 243-245, […] if you do any thing for charity, helpe me; if for neighborhood or brotherhood, helpe me […]
   Then the prison and the palace were in awful neighbourhood. 1835, Edward Bulwer-Lytton, Rienzi, the Last of the Roman Tribunes
7. (dated) Close proximity; nearness.
   At first he was partly hidden among the latschen, then his hind-quarters, quite black, emerged from the dark green bushes, as he slowly moved on, perfectly unconscious of our neighbourhood. 1853, Charles Boner, Chamois Hunting in the Mountains of Bavaria, page 286
8. (obsolete) The disposition becoming a neighbor; neighborly kindness or good will.
9. (topology) Within a topological space:
   1. A set containing an open set which contains some specified point.
   2. Alternatively: An open set which contains some specified point.
10. (topology) Within a metric space:
    1. A set containing an open ball which contains a specified point.
    2. Alternatively: An open ball which contains some specified point.
11. (topology) The infinitesimal open set of all points that may be reached directly from a given point.
12. (graph theory) The set of all the vertices adjacent to a given vertex.
    1. (cellular automata) The set of all cells near a given cell used to determine that cell's state in the next generation.
       In fact, it looks at the number of states and the neighborhood of the rule (determined by the filename), and decides whether to make it a lookup-table, or a "computed-function" rule. 1990-07-09, David Hiebeler, “Languages for programming cellular automata”, in comp.theory.cell-automata (Usenet)
       Universal: Is able to simulate other CA, the neighborhood size may be limited but the number of cell value should be unlimited (big neighborhoods can be transformed into multivalued cells). 2005-09-07, IzI, “reversible universal 1D CA?”, in comp.theory.cell-automata (Usenet)
       I've seen this space colloqually referred to as MAP (presumably since it maps a 3x3 neighborhood into a future cell state), or more precisely and if you want to be pedantic, since there are a lot of variants of cellular automata: 2D Range-1 Moore neighborhood 2-state (non-totalistic) cellular automata (regular euclidean grid implied, although some people explore toroidal configurations, nonstandard tilings, or arbitrary graphs). 2022-02-11, Mateon1, “Game of Life with real 8 neighbors”, in comp.theory.cell-automata (Usenet)