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## Due October 30

### Problem 1

Let $A\subset X$ be connected. Then $\bar A$ is connected.

### Problem 2

If $A\subset X$ is connected and $A\subset B\subset \bar A$, then $B$ is connected.

### Problem 3

$X$ is connected if and only if every continuous $f:X\to Y$ into a discrete space $Y$ is constant.

### Problem 4

If $A$ is convex, then $\bar A$ is convex.

### Problem 5

Prove $B_r(x_0)$ is convex from the fact that $B_1(0)$ is convex.