Sizing-agent-coated carbon fibers, process for producing sizing-agent-coated carbon fibers, carbon-fiber-reinforced composite material, and process for producing carbon-fiber-reinforced composite material

Sizing-agent-coated carbon fibers obtained by coating carbon fibers with a sizing agent comprising at least one of (A) to (C) in a total amount of 80 mass% or more with respect to the whole sizing agent, the carbon fibers each having a surface layer which has a thickness of 10 nm or larger and has an oxygen content of 4% or higher with respect to all the elements, wherein when the sizing-agent-coated carbon fibers are subjected three times to a 10-minute ultrasonic treatment in an acetone solvent, then the amount of the remaining sizing agent is 0.1-0.25 parts by mass per 100 parts by mass of the sizing-agent-coated carbon fibers. (A) At least one polymer selected from the group consisting of polyimides, polyetherimides, and polysulfones (B) A compound having a terminal unsaturated group and a polar group in the molecule (C) A polyether-type aliphatic epoxy compound and/or a polyol-type aliphatic epoxy compound which each have an epoxy equivalent of 250 g/eq or less and have two or more epoxy groups in the molecule