A point of a topological space is isolated if it is a neighbourhood of itself, in other words if the singleton subset is open.
More generally, a point of a subset of a space is isolated in if it is isolated when viewed as a point in the subspace with the subspace topology. More explicitly, for some neighbourhood of (in ), .
The antithetical concept is that of an accumulation point.
Every function on is continuous at if is isolated.
Created on June 28, 2020 at 09:04:41. See the history of this page for a list of all contributions to it.