Final answer:
The statement regarding Trilby being a man's hat with the top pressed down the middle is false; a Trilby has a narrow brim and indented crown, distinguishing it from the flat-crowned top hat which was a symbol of 19th-century bourgeoisie.
Step-by-step explanation:
The statement in question is false. A Trilby is indeed a type of hat, but it is not a top hat nor is it worn with the top part pressed down along the middle. The Trilby was made popular in the 20th century and is characterized by a narrower brim than a fedora and has an indented crown.
On the other hand, the top hat, often associated with 19th-century bourgeois fashion, was an iconic mark of class identity and featured a tall, flat-crowned shape, quite distinct from the later Trilby style.