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The frame envelope of a \(\sigma\)-frame. (English) Zbl 0779.06009
Summary: The universal frame extension of a \(\sigma\)-frame is studied, with particular attention to constructiveness and choice principles. In particular, the \(\sigma\)-frame coproduct is related to that of frames, providing a constructively valid proof of its compactness for compact \(\sigma\)-frames. Further, a \(\sigma\)-frame is shown to consist exactly of the Lindelöf elements of its frame envelope, and some consequences of this are explored.

MSC:
06D20 Heyting algebras (lattice-theoretic aspects)
54B10 Product spaces in general topology
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