Linked from

The 60 pages that link to Continuous function, each with the reason it gives.

• Urysohn's metrization theoremRelated: The constructed functions encode topological separation as real-valued data.

• General topologyRelated: Continuity is the central relation through which topological properties are compared.

• Ham sandwich theoremRelated: Continuity lets the balancing argument track how each side's measure changes with the cut.

• Iterated integralRelated: Continuity on suitable bounded regions provides familiar conditions for repeated integration.

• Slutsky's theoremRelated: Continuity supports the theorem’s extension to transformations beyond basic arithmetic.

• Hairy ball theoremRelated: Continuity prevents a tangent field from changing direction through a jump.

• Regula falsiRelated: Continuity makes opposite signs at interval endpoints evidence of an interior root.

• Peter–Weyl theoremRelated: Uniform density is asserted within the continuous functions on the group.

• Vector-valued functionRelated: Continuity of a vector-valued function can be checked in its components.

• Fundamental lemma of the calculus of variationsRelated: Continuity upgrades nonvanishing at one point to a neighborhood where a localized test detects it.