Definition
Epsilon Neighbourhood (Scalar)
The epsilon neighbourhood of a point
, denoted by , is the set of all points whose distance from is strictly less than : Geometrically, this corresponds to an open interval centred at
with radius .
Contextual Usage
- Convergence: A sequence
converges to if for every , the neighbourhood contains almost all terms of the sequence. - Continuity: A function
is continuous at if for every epsilon neighbourhood of , there exists a delta neighbourhood of such that . - Topological Definition: A set is open if every point in the set has an epsilon neighbourhood contained entirely within the set.