MathDB
Countable

Source: IMS 2006

July 12, 2006
functionlimittopologyadvanced fieldsadvanced fields unsolved

Problem Statement

Assume that XX is a seperable metric space. Prove that if f:X⟶Rf: X\longrightarrow\mathbb R is a function that lim⁡x→af(x)\lim_{x\rightarrow a}f(x) exists for each a∈Ra\in\mathbb R. Prove that set of points in which ff is not continuous is countable.
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