Linked from

The 14 pages that link to Connected space, each with the reason it gives.

• TopologyRelated: Connectedness captures whether a space falls apart under topological separation.

• Open setRelated: Open subsets express the separations that connectedness forbids.

• Topological spaceRelated: Connectedness detects whether the topology splits a space into separate pieces.

• Intermediate value theoremNarrower topic: The theorem follows because continuous images of connected sets remain connected.

• Maximum modulus principleRelated: Connectedness is needed to conclude that local constancy forces constancy throughout the domain.

• HomeomorphismRelated: Connectedness is preserved by homeomorphisms.

• Identity theoremNarrower topic: Connectedness lets local equality extend across the entire domain.

• Closed setCompared with: A nontrivial clopen subset separates a space, while closedness alone does not.

• Riemannian distanceRelated: Connectedness of a manifold ensures points can be joined by piecewise smooth curves.

• General topologyRelated: Connectedness captures an unbroken structure using only open sets.

• Bolzano's theoremRelated: The interval's connectedness explains why a continuous image cannot jump between opposite signs.

• Zero-dimensional spaceCompared with: A connected zero-dimensional space with a clopen basis must be a singleton.

• Harnack's principleRelated: Connectedness helps force the finite-versus-infinite alternative across the whole domain.

• Hilbert–Smith conjectureRelated: Connectedness is an explicit hypothesis in the conjecture.