Uniformly locally connected uniform σ-frames

Naidoo, Inderasan

doi:10.1007/s10474-008-8046-1

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2013

2023

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Cited by 2 publications

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References 12 publications

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“…An internal description of the Samuel compactification NR σ L of a nearness σ-frame is provided in [10]. A recent discussion in [14] provides for an alternative description of the compact regular coreflection of a nearness σ-frame. We use this illustration to bring together the completion, total boundedness, (super) strongness and the Samuel compactification in the realm of σ-frames.…”

Section: Introductionmentioning

confidence: 99%

On completion in the category SSNσFrm

Naidoo

2013

Mathematica Slovaca

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ABSTRACT. We introduce the category SSNσFrm of super strong nearness σ-frames and show the existence of a completion for a super strong nearness σ-frame unique up to isomorphism by the similar construction presented in Completion is also shown to be a coreflection in SSNσFrm. We also engage with the notion of total boundedness for nearness σ-frames and provide a characterization of the Samuel compactification of a nearness σ-frame alternative to the description in [NAIDOO, I.: Samuel compactification and uniform coreflection of nearness σ-frames, Czechoslovak Math.

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Section: Introductionmentioning

confidence: 99%

On completion in the category SSNσFrm

Naidoo

2013

Mathematica Slovaca

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Uniform Local Connectedness and Completion of Metric σ-Frames

Naidoo

2023

Mathematica Slovaca

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We extend the notion of local connectedness and uniform local connectedness to the category M σ Frm of metric σ-frames. We provide the construction of the uniformly locally connected reflection of a locally connected metric σ-frame. We also discuss complete metric σ-frames and show the existence of a completion for a metric σ-frame in the category M σ Frm.

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Uniformly locally connected uniform σ-frames

Abstract: We introduce and study the concept of a uniformly locally connected uniform σ-frame. The uniformly locally connected reection of a locally connected uniform σ-frame is constructed.

Cited by 2 publications

References 12 publications

On completion in the category SSNσFrm

On completion in the category SSNσFrm

Uniform Local Connectedness and Completion of Metric σ-Frames

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