I saw the symbol $\cup _f$ in the definition of "Cell attachment" in an algebraic topology notes, it says:
What does the symbol $\cup _f$ mean?
2026-03-26 18:58:54.1774551534
What does $\cup _f$ mean?
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This definition is defining the symbol, and the right hand side of the equation is what it means. You might pronounce it as "$X$ glued to D^n along $f$."
(Your photo doesn't include the definition of $\sim$ but that is also very important.)