Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 2G / iv / Solution

False. The coordinate axesare both closed nowhere dense subsets of ${\mathbb{R}}^2$, but every $(x,y)$ is $(x,0)+(0,y)$, sowhich is not meagre by the Baire category theorem.

Solved by gpt-5.6-sol high.