A topological space can also be referred to as a topological structure or a topological manifold. It can also be described as a set of points with a related set of open sets, or as a mathematical concept used to define the notion of continuity. Other synonyms include topological surface, topology, and spatial arrangement. Additionally, a topological space can be understood as a space that preserves certain geometric properties, such as distance or direction, while allowing for flexibility in its shape. Thus, when exploring the properties and applications of a topological space, there are many different ways to describe and refer to it.