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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.20835 |
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| _version_ | 1866917881277579264 |
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| author | Isaev, Valery |
| author_facet | Isaev, Valery |
| contents | In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete spaces. This subcategory is closely related to a particular subcategory of locales, offering an alternative approach to localic completion. Additionally, we demonstrate how this framework provides simple constructive definitions of compact spaces, uniform convergence, and limits of nets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20835 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Constructive Approach to Complete Spaces Isaev, Valery General Topology Category Theory 54E15 In this paper, we present a constructive generalization of metric and uniform spaces by introducing a new class of spaces, called cover spaces. These spaces form a topological concrete category with a full reflective subcategory of complete spaces. This subcategory is closely related to a particular subcategory of locales, offering an alternative approach to localic completion. Additionally, we demonstrate how this framework provides simple constructive definitions of compact spaces, uniform convergence, and limits of nets. |
| title | A Constructive Approach to Complete Spaces |
| topic | General Topology Category Theory 54E15 |
| url | https://arxiv.org/abs/2412.20835 |