open has 27 distinct synonyms spread across 22 of its 36 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its 3 recorded opposites are shut, closed, close.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
affording unobstructed entrance and exit; not shut or closed
“an open door”
affording free passage or access
“open drains”
(set theory) of an interval that contains neither of its endpoints
not brought to a conclusion; subject to further thought
“an open question”
openly straightforward and direct without reserve or secretiveness
“his candid eyes”
begin or set in action, of meetings, speeches, recitals, etc.
“He opened the meeting with a long speech”
make the opening move
“Kasparov opened with a standard opening”
where the air is unconfined
“he wanted to get outdoors a little”
a tournament in which both professionals and amateurs may play
information that has become public
“all the reports were out in the open”
8 of the 36 recorded senses carry no synonym, antonym or related term, so they are not shown above. Every sense, with its definition and examples, is on the full entry for open.
Synonyms, antonyms and the broader and narrower relations for open come from Princeton University’s WordNet. Full sources and licences.