Notes on Pointfree Disconnectivity with a Ring-theoretic Slant

作者：Dube Themba^*

来源：Applied Categorical Structures, 2010, 18(1): 55-72.

DOI：10.1007/s10485-008-9162-3

• Frame
• F-frame
• Basically disconnected
• Extremally disconnected
• Ring of continuous functions on a frame
• Ring-ideal
• Large compactification

We give characterizations of extremally disconnected frames, basically disconnected frames and F-frames L in terms of ring-theoretic properties of the ring RL of continuous real-valued functions on L. Emanating from these are new (and purely ring-theoretic) proofs that a frame is extremally disconnected, basically disconnected or an F-frame iff the same holds for its Cech-Stone compactification.

• 出版日期2010-2