neighborhood

noun

• The quality of being a neighbor, of living nearby, next to each-other; proximity.

  "Our neighborhood was our only reason to exchange hollow greetings."

• Close proximity, nearby area; particularly, close proximity to one's home.

  "He lives in my neighborhood."

• The inhabitants of a residential area.

  "The fire alarmed the neighborhood."

• A formal or informal division of a municipality or region.

  "We have just moved to a pleasant neighborhood."

• An approximate amount.

  "He must be making in the neighborhood of $200,000 per year."

• The quality of physical proximity.

  "The slums and the palace were in awful neighborhood."

• The disposition becoming a neighbor; neighborly kindness or good will.
• Within a topological space:
• Within a metric space:
• The infinitesimal open set of all points that may be reached directly from a given point.
• The set of all the vertices adjacent to a given vertex.