user43901
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### Questions (36)

 5 Existence of an improper integral without the existence of a limit 5 If the graph of a function $f: A \rightarrow \mathbb R$ is compact, is $f$ continuous where $A$ is a compact metric space? 5 How is Cantor's diagonal argument related to Russell's paradox in naive set theory? 5 $\sin(1/x)$ not uniformly continuous 4 What is the interior of a singleton?

### Reputation (498)

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 4 If every subset of $M$ is clopen, then show that any function $f: M \rightarrow N$ is continuous where M and N are metric spaces 3 Suppose $M$ is connected and suppose $f : M \rightarrow \mathbb R$ is continuous and only has irrational values, then $f$ is a constant function.

### Tags (20)

 7 general-topology × 13 0 integration × 7 3 real-analysis × 22 0 elementary-set-theory × 5 3 connectedness × 3 0 derivatives × 5 3 continuity × 2 0 compactness × 5 0 calculus × 9 0 dynamical-systems × 3

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 Mathematics 498 rep 319 Stack Overflow 101 rep 1