Topological Spaces-Topological Spaces

Dentition :A topological space X consists of a set X together with a collection of subsets, referred to as open sets, such that the following conditions are satisfied:

(i) the empty set ∅ and the whole set X are open sets,

(ii) the union of any collection of open sets is itself an open set,

(iii) the intersection of any finite collection of open sets is itself an open set.

The collection consisting of all the open sets in a topological space X is referred to as a topology on the set X.