Usually means: Covers all elements of codomain.
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Similar:
INTO, down, across, back, through, towards, directly, From, accross, underneath, more...

Opposite:
off, away, from, from, out, of, detached

Types:
one-to-one, surjective, injective, bijective, more...

Meter:

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Crossword clues:
on to,   latch (grasp),   on to something,   glom (grab),   latch (seize)

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