Linked from

The 36 pages that link to Topological space, each with the reason it gives.

• Metric spaceNarrower topic: A metric induces a topology, but topology forgets specific distance values.

• TopologyBroader topic: This is the basic mathematical object whose properties topology studies.

• Compact spaceNarrower topic: Compactness is defined using the open sets of this underlying structure.

• Open setRelated: Its axioms govern unions and finite intersections of open sets.

• Fundamental groupNarrower topic: The loops and their deformations live in this underlying space.

• HomeomorphismNarrower topic: Homeomorphisms compare spaces through their open sets rather than distances.

• Algebraic topologyNarrower topic: Algebraic topology begins with spaces whose continuous deformations preserve the features its invariants measure.

• Closed setNarrower topic: Closedness is defined relative to the topology on this space.

• Hausdorff spaceNarrower topic: Hausdorff separation is an additional condition imposed on a topological space.

• ManifoldNarrower topic: Manifolds add local Euclidean structure to the more general notion of topological space.

• Alexander GrothendieckNarrower topic: Grothendieck generalized the role of topology through sites and Grothendieck topologies.

• Connected spaceNarrower topic: Connectedness is defined by how the open subsets of a topological space can partition it.

• Homology groupNarrower topic: Homology assigns algebraic invariants to spaces while remaining insensitive to continuous deformation.

• Open coverNarrower topic: Open covers are defined using the open sets of a topological space.

• Measure spaceCompared with: Topology identifies open sets, while a measure space identifies measurable sets and their sizes.

• Borel measureNarrower topic: Its open sets determine the Borel sets available to the measure.

• Boundary (topology)Narrower topic: Boundaries are defined relative to the open sets of an ambient space.

• ConvergenceNarrower topic: Neighborhoods define convergence even when no distance is available.

• HomotopyNarrower topic: The domain and codomain of a homotopy are topological spaces.

• Subspace topologyNarrower topic: The subspace construction starts with an ambient topological space.

• Convergent sequenceNarrower topic: Neighborhood-based convergence is defined using the topology of the space.

• Homotopy equivalenceNarrower topic: Homotopy equivalence compares spaces through continuous maps.

• Sequential compactnessNarrower topic: Sequential compactness is a property of topological spaces.

• Normal spaceNarrower topic: Normality is a property of this underlying structure.

• Sierpiński spaceNarrower topic: Sierpiński space is a finite, minimal example of a topological space.

• Vector bundleNarrower topic: The base and total spaces use topology to express continuity and local resemblance.

• Felix HausdorffRelated: His foundational work gave a systematic framework for such spaces.

• Möbius stripNarrower topic: The Möbius strip is studied by properties preserved under continuous deformation.

• Separation axiomNarrower topic: Separation axioms impose additional conditions on this underlying structure.

• Urysohn's lemmaNarrower topic: The lemma is stated for spaces whose open sets determine continuity and separation.

• Order theoryRelated: Open sets form a lattice ordered by inclusion, linking topology to order.

• Tietze extension theoremNarrower topic: The theorem concerns continuous functions and closed subsets within this general setting.

• General topologyBroader topic: This is the basic object whose properties general topology studies.

• Tube lemmaNarrower topic: The lemma applies to arbitrary topological spaces, not only metric spaces.

• 3-manifoldNarrower topic: A 3-manifold is a topological space with a specific local form.

• Kuratowski's closure-complement problemNarrower topic: Closure is defined relative to the topology on the underlying space.