# I don't understand the meaning of “trace” in this context

I'm not a native English speaker and I found in an old book I'm using for research the word "trace" as it follows:

It appears several times in the book, but when I look for its meaning on the Internet, I only found it referred to the trace of a matrix.

Can anyone explain what does it mean?

• I believe this is defined in Bourbaki's chapters on set theory in a more general setting. Use the index to find definitions. I see from the typeface and terminology that you're using Bourbaki: for topology, the set theory chapters are assumed to be known. – Henno Brandsma Dec 29 '18 at 12:56
• It is Bourbaki indeed. But it happens that I only have the topology one. And of course I tried to find the definition in the book itself, but it isn't there. That's why I asked. But I really didn't think of looking on his other books. – Ismael Manzanares Carmona Dec 31 '18 at 18:23

The trace of a family $$\mathscr F$$ of subsets of a set $$X$$ on a subset $$A$$ is the family$$\{F\cap A\,|\,F\in\mathscr{F}\}.$$