That subset of a set of 1st category (can write as countable union of nowhere dense sets) is also 1st category? Intuitively it is clear, but I am not sure how to argue formally Thank you for helping
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Originally Posted by MMath09 That subset of a set of 1st category (can write as countable union of nowhere dense sets) is also 1st category? If X is of category I then where each is nowhere dense.
Originally Posted by Plato If X is of category I then where each is nowhere dense. Is this last bit supposed to be ? So you write the set X as the union of the set X and the subset B So if B was made up of somewhere dense sets or an uncountable number of sets then you could write X like that too & that would be a contradiction OK thanks