3 added 491 characters in body

Many existence proofs which exploit the idea of Baire category.

For instance, existence of a metrically transitive automorphism of the closed unit square was first obtained by the category method (see, e.g., see "Measure-preserving homeomorphisms and metrical transitivity" by Oxtoby and Ulam) . Another classical example is due to Banach who proved that every function from a residual subset of $C[0,1]$ is nowhere differentiable.

A nice and elementary book by Oxtoby where he discusses this these and many other applications of the category method)method.

2 added 524 characters in body

Many existence proofs which exploit the idea of Baire category.

For instance, existence of a metrically transitive automorphism of the closed unit square was first obtained by the category method (see, e.g., a nice and elementary book by Oxtoby where he discusses this and other applications of the category method).

1

Many existence proofs which exploit the idea of Baire category.