early 13c., "an aperture or opening," from open (adj.). Sense of "an open or clear space" is by 1796. The open "open country" is from 1620s; as "open air" from 1875. Meaning "public knowledge" (especially in out in the open) is from 1942, but compare Middle English in open (late 14c.) "manifestly, publicly." The sense of "an open competition" is from 1926, originally in a golf context.
Old English openian "to open, open up, cause to open, disclose, reveal," also intransitive, "become manifest, be open to or exposed to," from Proto-Germanic *opanojan (source also of Old Saxon opanon, Old Norse opna "to open," Middle Dutch, Dutch openen, Old High German offanon, German öffnen), from the source of open (adj.), but etymology suggests the adjective is older. Transitive sense of "set in action, begin, commence" is from 1690s. Open up (intrans.) in the figurative sense "cease to be secretive" is from 1921. Related: Opened; opening.
Old English open "not closed down, raised up" (of gates, eyelids, etc.), also "exposed, evident, well-known, public," often in a bad sense, "notorious, shameless;" from Proto-Germanic *upana-, literally "put or set up" (source also of Old Norse opinn, Swedish öppen, Danish aaben, Old Saxon opan, Old Frisian epen, Old High German offan, German offen "open"), from PIE root *upo "under," also "up from under," hence also "over." Related to up, and throughout Germanic the word has the appearance of a past participle of *up (v.), but no such verb has been found. The source of words for "open" in many Indo-European languages seems to be an opposite of the word for "closed, shut" (such as Gothic uslukan).
Of physical spaces, "unobstructed, unencumbered," c. 1200; of rooms with unclosed entrances, c. 1300; of wounds, late 14c. Transferred sense of "frank, candid" is attested from early 14c. Of shops, etc., "available for business," it dates from 1824.
Open-door in reference to international trading policies is attested from 1856. Open season is recorded by 1895 of game; figuratively (of persons) by 1914. Open book in the figurative sense of "person easy to understand" is from 1853. Open house "hospitality for all visitors" is first recorded 1824. Open-and-shut "simple, straightforward" first recorded 1841 in New Orleans. Open-faced, of sandwiches, etc., "without an upper layer of bread, etc.," by 1934. Open marriage, one in which the partners sleep with whomever they please, is by 1972. Open road (1817, American English) originally meant a public one; romanticized sense of "traveling as an expression of personal freedom" first recorded 1856, in Whitman.
also openminded, "having an unreserved mind; frank, candid," also "having a mind accessible to new views, not narrow-minded, unprejudiced," 1828, first recorded in Carlyle; from open (adj.) + -minded. Figurative use of open (adj.) with reference to hearts, hands, etc. is from early 15c. Related: Open-mindedly; open-mindedness.
Could we hope that, in its present disjointed state, this emblematic sketch ["Wanderjahre"] would rise before the minds of our readers, in any measure as it stood before the mind of the writer; that, in considering it, they might seize only an outline of those many meanings which, at less or greater depth, lie hidden under it, we should anticipate their thanks for having, a first or a second time, brought it before them. As it is, believing that to open-minded, truth-seeking men, the deliberate words of an open-minded, truth-seeking man can in no case be wholly unintelligible, nor the words of such a man, as Goethe, indifferent, we have transcribed it for their perusal. [Carlyle, "Goethe," 1828]
late 13c., "furnace;" late 14c., "smoke vent of a fireplace, vertical structure raised above a house for smoke to escape to the open air;" from Old French cheminee "fireplace; room with a fireplace; hearth; chimney stack" (12c., Modern French cheminée), from Medieval Latin caminata "a fireplace," from Late Latin (camera) caminata "fireplace; room with a fireplace," from Latin caminatus, adjective of caminus "furnace, forge; hearth, oven; flue," from Greek kaminos "furnace, oven, brick kiln," which is of uncertain origin.
From the persistence of the medial i in OF. it is seen that the word was not an ancient popular word, but a very early adoption of caminata with subsequent phonetic evolution [OED]
Middle English also had native names for it: smokethurl, smokehole (14c.). Jamieson  notes that in vulgar use in Scotland it typically was pronounced "chimley." From the same source are Old High German cheminata, German Kamin, Russian kaminu, Polish komin. Chimney-corner "space beside a fireplace" is from 1570s.
"lobby of a theater or opera house," 1859, from French foyer "green room, room for actors when not on stage," literally "fireplace," from Old French foier "furnace, stove, hearth, fireplace" (12c.), from Latin focarium, noun use of neuter of adjective focarius "having to do with the hearth," from focus "hearth, fireplace" (see focus (n.)).