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Motivated by works on extension sets in standard domains we introduce anotion of the Carath\'eodory set that seems better suited for the methods usedin proofs of results on characterization of extension sets. A special stress isput on a class of two dimensional submanifolds in the tridisc which not onlyturns out to be Carath\'eodory but also provides examples of two dimensionaldomains for which the celebrated Lempert Theorem holds. Additionally, arecently introduced notion of universal sets for the Carath\'eodory extremalproblem is studied and new results on domains admitting (no) finite universalsets are given.

Extension property in the tridisc