firmly, tightly
He closed the door firmly.

gently, quietly, silently, softly
She gently closed the door behind her.

permanently, temporarily
officially
Tomorrow college officially closes for the vacation.

down, off, up
That factory's been closed down now.

to
The museum has been temporarily closed to the public.

be
come, draw, get, move
She grew increasingly nervous as the audition drew closer.

keep, stay
Keep close to me.

hold sb, hug sb, pull sb

extremely, remarkably, very
fairly, quite, reasonably, relatively
awfully (esp. AmE), dangerously, frighteningly, perilously, precariously, uncomfortably
The car came perilously close to running her down.

tantalizingly
Victory was tantalizingly close.

geographically
together
Their birthdays are very close together.

to
Get close to the microphone.

be, feel, seem
The two sisters seemed very close.

become, grow
After the death of their parents the two children grew very close.

bring sb
These horrific events brought the family closer.

remain

very
quite

to
He was very close to his older brother.

Close is used with these nouns:
acquaintance, adherence, adviser, affinity, aide, alignment, alliance, ally, analogy, analysis, approximation, associate, association, attachment, attention, bond, call, check, circle, collaboration, colleague, combat, communion, community, companion, companionship, comparison, confinement, confines, connection, consultation, contact, contest, control, cooperation, coordination, correlation, correspondence, cousin, dialogue, election, embrace, encounter, escape, examination, eye, family, fight, finish, fit, follower, formation, friend, friendship, game, guard, imitation, inspection, integration, interest, intimacy, investigation, involvement, kin, liaison, link, look, monitoring, neighbour, observation, observer, parallel, partnership, proximity, pursuit, questioning, race, range, rapport, reading, relation, relationship, relative, resemblance, rival, score, scrutiny, season, shave, similarity, study, substitute, supervision, supporter, surveillance, thing, tie, touch, union, vicinity, view, vote, watch