The Daily Trap
One Part C question, the same one for everyone, every morning. Four statements, four true-or-false calls — and like the real paper, only the exact correct set scores. No account, no sign-up.
Daily Trap · No. 52
Topology › Connectedness and components
Let X be a topological space and, for x ∈ X, let C(x) denote the connected component of x. Which of the following are true?
C(x) is always closed in X.
All four count. Part C scores only for the exact correct set.
Why one wrong call costs the whole question
Part C is worth 4.75 marks a question with no negative marking, and you may attempt 20 of the 60. What makes it hard is the rule underneath: credit only for selecting exactly the right set of options. A question you are three-quarters sure of pays the same as one you did not read — which is why judging statements one at a time is the skill worth practising, and why this puzzle marks them that way.
- Want more than one a day? The statement drill runs unlimited single statements and tells you which mistake you keep making.
- The claims behind most traps live in the counterexample bank.
- Or sit a whole paper: every previous-year question, solved.