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A note on S-metrizable frames. (English) Zbl 1508.06007

Summary: A metric frame \((M,d)\) is S-metrizable if there exists a compatible metric diameter \(\rho\) on \(M\) such that \((M,\rho)\) has property S. The latter concept of property S was introduced to frames by D. Baboolal [Appl. Categ. Struct. 8, No. 1–2, 377–390 (2000; Zbl 0969.54004)]. Given a connected, locally connected metric frame \((M,d)\), we show that \((M,d)\) is S-metrizable if and only if \((M,d)\) has a perfect locally connected metrizable compactification.

MSC:

06D22 Frames, locales
54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
54E35 Metric spaces, metrizability

Citations:

Zbl 0969.54004
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References:

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