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Sahithyan's S1
Sahithyan's S1 -- Maths

Continuity

A function is continuous at iff:

One-side continuous

Continuous from left

A function is continuous from left at iff:

Continuous from right

A function is continuous from right at iff:

On interval

Open interval

A function is continuous in iff is continuous on every .

Closed interval

A function is continuous in iff is:

  • continuous on every
  • right-continuous at
  • left-continuous at

Uniformly continuous

Suppose a function is continuous on . is uniformly continuous on iff:

If a function is continuous on , is uniformly continuous on .