Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.24997 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917049147588608 |
|---|---|
| author | Gemaledin, Ismail Gemaledin, Iusuf |
| author_facet | Gemaledin, Ismail Gemaledin, Iusuf |
| contents | Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an elementary exposition of metric spaces and their associated topologies. We start by recalling the basic axioms through which we understand a metric and examine various examples. The induced topology is next discussed with emphasis on open and closed sets, continuity and limits. In addition, we compare equivalent metric spaces and illustrate how different metrics can generate but the same topological structure. The presentation is designed to be easy to follow and accessible to undergraduate students, by combining classical definitions with illustrative examples that allow a deeper understanding of the aforementioned concepts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24997 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Elementary Expository Study: From Metric Spaces to Hilbert Spaces Gemaledin, Ismail Gemaledin, Iusuf General Topology Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an elementary exposition of metric spaces and their associated topologies. We start by recalling the basic axioms through which we understand a metric and examine various examples. The induced topology is next discussed with emphasis on open and closed sets, continuity and limits. In addition, we compare equivalent metric spaces and illustrate how different metrics can generate but the same topological structure. The presentation is designed to be easy to follow and accessible to undergraduate students, by combining classical definitions with illustrative examples that allow a deeper understanding of the aforementioned concepts. |
| title | An Elementary Expository Study: From Metric Spaces to Hilbert Spaces |
| topic | General Topology |
| url | https://arxiv.org/abs/2510.24997 |