What is this symbol?

Question

I am reading "Sets, Numbers and Topology" by Masahiko Saito.
And the following symbol is used to denote the set of equivalence classes in the book.

What is this symbol?
$J$?
$T$?

Answer 1

It is a calligraphic F. The closest looking I know for use with LaTeX is the dutchcal font (available on CTAN):

Answer 2

I suspect it is based on a Fraktur F, like or $\mathfrak{F}$

In MathJax, you can use \mathfrak{F}

Answer 3

I belive it represents the Fourier transform. I use it frequently and am always fighting font types and editors to try to get it to render nicely.