There is a notation that had an immediate and profound impact on research in algebraic topology, later algebraic geometry, and was eventually adopted by all areas of pure mathematics: the introduction of arrows to denote mappings. Compare $f \colon X \to Y$ with $f(X) \subset Y$, which is what was used previously.

The use of arrows led to commutative diagrams, without which many parts of modern mathematics are now inconceivable. I mentioned this before in an answer here.

There is a notation that had an immediate and profound impact on research in algebraic topology, later algebraic geometry, and was eventually adopted by all areas of mathematics: the introduction of arrows to denote mappings. Compare $f \colon X \to Y$ with $f(X) \subset Y$, which is what was used previously. It meets all three criteria mentioned by the OP and is recognized by every mathematician.

Just as importantly, the use of arrows led to commutative diagrams, without which many parts of modern mathematics are now inconceivable. I mentioned this before in an answer here.