In topology, a 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. These axioms allow us to define concepts like open and closed sets, which in turn allow us to define continuity and other important topological notions.

There are many different types of spaces that can be studied in topology, ranging from simple spaces like the real numbers or the unit circle, to more complex spaces like manifolds or topological groups. The specific structure of a space depends on the particular axioms that are used to define it, and different spaces can have very different properties and behaviors.

In general, the study of topology is concerned with understanding the inherent structure of spaces and the continuous functions that map between them. This includes studying properties like connectivity, compactness, and separation, as well as the topological invariants that can be used to classify different spaces and functions.