Question

Can we define limit point in terms of open sets in topology

Answer 1

Answer:

In mathematics, a limit point (or cluster point or accumulation point) of a set {\displaystyle S} in a topological space {\displaystyle X} is a point {\displaystyle x} that can be "approximated" by points of {\displaystyle S} in the sense that every neighbourhood of {\displaystyle x} with respect to the topology on {\displaystyle X} also contains a point of {\displaystyle S} other than {\displaystyle x} itself. A limit point of a set {\displaystyle S} does not itself have to be an element of {\displaystyle S} .