Math 2.0

Real functions Concept

Continuity in R^n

Builds on Limit of a function of several variablesEuclidean space

Summary

Take a function between subsets of Euclidean spaces, and a point aa. The function is continuous at this point when small changes of the input near aa give small changes of the value. For a function of several variables, the input can change in all coordinates at once.

Reading path

To understand this page from the ground up, read these 5 pages in order. The foundations come first.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptLimit of a function of several variables, concept, no evidence levelLimit of a function o…conceptContinuity in R^n, concept, no evidence levelContinuity in R^nconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Function of several variables concept
  4. Limit of a function of several variables concept
  5. Continuity in R^n concept

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Continuous_function, Continuous functions between metric spaces
About this page
Tag0JEJATBVD7
URIm2://0JEJATBVD7
Aliasescontinuous-function-of-several-variables, multivariable-continuity
Kindconcept
WritingW0 stub
MSC26B05
UsesLimit of a function of several variables, Euclidean space

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