Connected fibres plus open map gives connected

Which of the following statements is true?

A.{m + ne $^(2\pi{}i/3)$ | $m, n \in \mathbb{Z}$ } is a dense subset of $\mathbb{C}$ .
B.Open connected subsets of $\mathbb{R}^{3}$ need not be path-connected.
C.Let X be a topological space and $p : X \to \mathbb{R} a$ continuous surjective open map. If p⁻ $^{1}($ { $\alpha$ }) is connected for every $\alpha \in \mathbb{R}$ , then X must be connected.✓ Correct
D.Compact subsets of any infinite topological space are closed.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests hypothesis dropped.

See pricing

50 are analysed free — try those first.

The trap it tests

Hypothesis dropped

A theorem applied without checking one of its preconditions.

Drill statements like this

Last revised 12 Sept 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.