Uniform local connectedness and completion of metric \(\sigma\)-frames

DOI10.1515/ms-2023-0100OpenAlexW4389886388MaRDI QIDQ6180423

Inderasan Naidoo

Publication date: 19 January 2024

Published in: Mathematica Slovaca (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ms-2023-0100

zbMATH Keywords

completionseparablecompleteconnectedLindelöf\(\sigma\)-frameuniform and metric \(\sigma\)-frameuniformly locally connected frame

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Frames, locales (06D22) Extensions of spaces (compactifications, supercompactifications, completions, etc.) (54D35) Connected and locally connected spaces (general aspects) (54D05) Uniform structures and generalizations (54E15) Preorders, orders, domains and lattices (viewed as categories) (18B35)

Cites Work

• Compactification and local connectedness of frames
• Connectedness extended to \(\sigma\)-frames
• Complete nearness \(\sigma\)-frames
• Uniformly locally connected uniform \(\sigma\)-frames
• Metric and complete metric \({\sigma}\)-frames
• A Shirota theorem for frames
• Local connectedness made uniform
• Connectedness in metric frames
• Universal locally connected refinements
• Samuel compactification and completion of uniform frames
• ON THE COMPLETION OF NEARNESS FRAMES
• CAUCHY POINTS OF UNIFORM AND NEARNESS FRAMES
• On completion in the category SSNσFrm
• THE FRAME ENVELOPE OF A σ-FRAME
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