Part BCSIR NET December 2024connected-fibres-plus-open-map-gives-connected

Connected fibres plus open map gives connected

Which of the following statements is true?

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

50 are analysed free — try those first.