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- #1

$\tau_Y=\left\{U\subseteq Y:\bigcup U =\left(\bigcup_{ {[a]\in U} }[a]\right)\in\tau_X\right\}$

be written

$\tau_Y=\left\{U\subseteq Y:\bigcup U =\left(\bigcup_{ {[a]\in U} }\left\{[a]\right\}\right)\in\tau_X\right\}$

instead?

since $\bigcup U=\bigcup_{ [a]\in U }\left\{[a]\right\}$

or is this not correct?

Wolfram mathworld writes it as $\bigcup_{ [a]\in U } a$ which doesn't make any sense to me. I've never really felt comfortable with these formulas.