I am wondering why a standard notation for open sets is $G$ and that for closed sets is $F$. I mean, $F$ precedes $G$ in the alphabet, whereas open sets are usually introduced before closed ones.



Notations for open and closed sets
I see that @LSpice has already provided an answer in their comment (I see that Emil has added a clarification, so to speak). Mine will compliment the comment by @LSpice a little.


Historically, closed sets were before the open sets (I believe so). Kazimierz Kuratowski defined topology (of general $T\_1$-spaces} via the closure operation hence the closed sets came before open sets. We are talking here about the years 1921 and 1933.


I seem to remember that also Wacław Sierpiński was introducing the closed sets before open sets.


Earlier, I believe, that topologists/mathematicians were talking about **neighborhoods** rather than open sets. Perhaps(?) people started to talk about open sets seriously only after the results/papers by Paul S. Urysohn (I am not a historian -- please, do double-check my vague reminiscences).


Finally, the notation F (for closed sets) comes from the French "Fermé"; then open G followed. In the old days, French and German were ruling mathematics before English.




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**SOURCES:**


* Hausdorff definition of topological spaces via neighborhoods:


$\qquad$https://mathworld.wolfram.com/HausdorffAxioms.html


See also Bourbaki foundational text on General Topology, it presents the Hausdorff neighborhood axioms soon after the today standard definition via open sets.


Hausdorff gutsy topological axioms absorbed Hilbert's axioms on 2d-geometric spaces.


