Understanding Analysis by Stephen Abbott

Author:Stephen Abbott
Language: eng
Format: epub, pdf
Publisher: Springer New York, New York, NY

(iii)If does not exist for some other reason, then the discontinuity at c is called an essential discontinuity.

We are now equipped to characterize the set D f for an arbitrary monotone function f.

Exercise 4.6.5.

Prove that the only type of discontinuity a monotone function can have is a jump discontinuity.

Exercise 4.6.6.

Construct a bijection between the set of jump discontinuities of a monotone function f and a subset of . Conclude that D f for a monotone function f must either be finite or countable, but not uncountable.

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