A topological space is a set of points that is equipped with a set of rules, called topological axioms, that describe how those points can be "clumped" together or "separated" from one another. 

In topology, open sets are often thought of as representing sets of points that are "far apart" from one another, while closed sets are thought of as representing sets of points that are "close together". This is because open sets are defined in terms of the topological axioms of a space, which describe how points in the space can be separated from one another.

Intuitively, an open set is a set of points that does not contain any "boundary" or "edge" points, which means that the points in the set are "far apart" from one another in some sense. This is in contrast to a closed set, which is defined as the complement of an open set and therefore includes all of the boundary points of the open set. This means that the points in a closed set are "close together" in the sense that they are all contained within a finite region that has a well-defined boundary.

Of course, the concepts of "far apart" and "close together" are somewhat subjective and depend on the specific topological space being considered. However, in general, open sets are thought of as representing sets of points that are more spread out or "loosely connected", while closed sets are thought of as representing sets of points that are more densely packed or "tightly connected".

Let me add some definitions that are touched on in the above description.

1. Open set: An open set in a topological space is a subset of the space that contains an open neighborhood around each of its points.

2. Closed set: A closed set in a topological space is a subset of the space that contains all of its limit points.

3. Boundary: The boundary of a set in a topological space is the set of points that are in the closure of the set, but not in the set itself.

4. Closure: The closure of a set in a topological space is the smallest closed set that contains the set.

5. Interior: The interior of a set in a topological space is the largest open set contained in the set.

6. Exterior: The exterior of a set in a topological space is the complement of the closure of the set.