topological space
nounA topological space is a math idea that describes how points in a set are connected to each other.
The teacher explained that a circle and a square are the same kind of shape in a topological space.
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OTHER MEANINGS
2. A set together with a collection of open subsets that satisfies the axioms of a topology.
Every metric space gives rise to a topological space whose open sets are the metric open balls.
3. A mathematical object studied in topology, defined by its open sets rather than by distances.
Two topological spaces are homeomorphic if there is a continuous bijection with a continuous inverse between them.
4. A foundational concept in point-set topology used to define continuity, connectedness, and compactness.
Continuity of a function between topological spaces means that preimages of open sets are open.