Definition of "neighborhood"

neighborhood

/ˈneɪbə.hʊd/

noun
countable and uncountable, plural neighborhoods
1. The residential area near one's home.
2. The inhabitants of a residential area.
3. A formal or informal division of a municipality or region.
4. An approximate amount.
5. The quality of physical proximity.
6. (chiefly obsolete) The quality of being a neighbor, of living nearby, next to each-other; proximity.
  Quotations
  […] if you do any thing for charity, helpe me; if for neighborhood or brotherhood, helpe me […]
  1595, George Peele, The Old Wives’ Tale, The Malone Society Reprints, 1908, lines 243-245
  Take her, fair son, and from her blood raise upIssue to me; that the contending kingdomsOf France and England, whose very shores look paleWith envy of each other’s happiness,May cease their hatred; and this dear conjunctionPlant neighbourhood and Christian-like accordIn their sweet bosoms […]
  1599, William Shakespeare, “The Life of Henry the Fift”, in Mr. William Shakespeares Comedies, Histories, & Tragedies […] (First Folio), London: […] Isaac Iaggard, and Ed[ward] Blount, published 1623, [Act V, scene ii]
  Nor content with such / Audacious neighbourhood, the wisest heart / Of Solomon he led by fraud to build / His Temple right against the Temple of God.
  1667, John Milton, “Book I”, in Paradise Lost. […], London: […] [Samuel Simmons], […]; republished as Paradise Lost in Ten Books: […], London: Basil Montagu Pickering […], 1873,
  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.
  Quotations
  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.
    Quotations
    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 July 9, 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 September 7, 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 February 11, Mateon1, “Game of Life with real 8 neighbors”, in comp.theory.cell-automata‎ (Usenet)