Topological Space (Noun)
Meaning
(mathematics) any set of points that satisfy a set of postulates of some kind; "assume that the topological space is finite dimensional".
Classification
Nouns denoting groupings of people or objects.
Examples
- A topological space is often thought of as a geometric object, such as a sphere or a torus, that has been stripped of its geometric structure.
- In the context of topology, a topological space is defined as a set of points that satisfy certain postulates, such as the existence of open sets.
- The real line with the standard topology is a fundamental example of a topological space that is both connected and locally connected.
- A Hausdorff topological space is a space in which any two distinct points can be separated by disjoint open sets.
- Assume that the topological space is finite dimensional, meaning that it can be covered by a finite number of open sets.