Bornological Approach Nearness

Dieter Leseberg; Zohreh Vaziry

doi:10.3390/ijt2030012

August 7, 2025Deleted JournalOpen Access

Bornological Approach Nearness

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Key Points

The generalized completion of nearness structures enhances the understanding of nearness spaces, and it integrates bornological concepts.
Key findings indicate that the new framework modifies criteria for compactness within approach spaces, improving existing theorems.
The study introduces bornological approach nearness, which unifies classical nearness structures and broadens their applicability.
Implications may extend to various domains in mathematical analysis, showcasing the interplay between boundedness and nearness.

Implication

This framework redefines completeness and extends compactness criteria in nearness spaces, suggesting new methods.

Abstract

We introduce the notion of bornological approach nearness as a unified extension of various classical nearness structures. By redefining completeness within this framework, we establish a generalized version of the Niemytzki–Tychonoff theorem. Our results not only extend known compactness criteria in nearness spaces but also offer a new perspective that incorporates boundedness and bornological methods in the theory of approach spaces.

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Cite This Study

Leseberg et al. (2025) studied this question.

synapsesocial.com/papers/68a366a80a429f797332caaa https://doi.org/10.3390/ijt2030012

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Bornological Approach Nearness

Key Points

Implication

Abstract

Discussion

Cite This Study

Bornological Approach Nearness

Key Points

Implication

Abstract

Discussion

Cite This Study

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