What does topological space mean?

Solution:

A topological space is the most general type of mathematical space that allows for the definition of limits, continuity, and connectedness.

A topological space is a set with a collection of subsets that satisfies the conditions that both the empty set and the set itself belong to the collection, the union of any number of the subsets is also an element of the collection, and the intersection of any finite number of the subsets is an element of the collection.

Let x = null set, a topology on x is a collection of "open subsets" of x which satisfy the following:

1) x, null set are open.

2) The union of any family of open sets is open.

3) The finite intersection of any collection of open sets is open. 

Hence, a space with an associated family of subsets that constitutes topology is known as a topological space.

What does topological space mean?

Summary:

A space with an associated family of subsets that constitutes topology.