# topology

Published articles for topology.

This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles.

## My Graduate Career in Math

DevFeed: [My Graduate Career in Math](<https://devfeed.tech/articles/my-graduate-career-in-math-40490.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2025/05/12/my-graduate-career-in-math/>)

Published: 2025-05-12T18:35:57Z

Content type: opinion

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Computer science](<https://devfeed.tech/topics/computer-science.md>), [graph theory](<https://devfeed.tech/topics/graph-theory.md>)

Tags: [computer-science](<https://devfeed.tech/tags/computer-science.md>), [education](<https://devfeed.tech/tags/education.md>), [essay](<https://devfeed.tech/tags/essay.md>), [essays](<https://devfeed.tech/tags/essays.md>), [game-theory](<https://devfeed.tech/tags/game-theory.md>), [graph-theory](<https://devfeed.tech/tags/graph-theory.md>), [group-theory](<https://devfeed.tech/tags/group-theory.md>), [linear-algebra](<https://devfeed.tech/tags/linear-algebra.md>), [math](<https://devfeed.tech/tags/math.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [retrospective](<https://devfeed.tech/tags/retrospective.md>), [topology](<https://devfeed.tech/tags/topology.md>), [university](<https://devfeed.tech/tags/university.md>)

### AI overview

An autobiographical essay about the author's transition from computer science to mathematics at Cal Poly, including university coursework, study abroad in Budapest, and reflections on the intellectual environment and an early group theory project.

### Source excerpt

Editor's note: This essay was originally published on Medium on 2016-03-05. I have made minor edits in this republishing and added a few small retrospective notes. 2010-2011 (Year 0) I had just switched my major at Cal Poly State University from computer science to math. I wanted to double major but California was in a budget crisis and a few weeks before I tried submitting my double-major request the Provost for the CSU system put a blanket ban on double majors.

## Constructing Topological Spaces -- A Primer

DevFeed: [Constructing Topological Spaces -- A Primer](<https://devfeed.tech/articles/constructing-topological-spaces-a-primer-40292.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/11/11/constructing-topological-spaces-a-primer/>)

Published: 2012-11-11T18:13:58Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [spaces](<https://devfeed.tech/topics/spaces.md>)

Tags: [building](<https://devfeed.tech/tags/building.md>), [complex](<https://devfeed.tech/tags/complex.md>), [dimension](<https://devfeed.tech/tags/dimension.md>), [quotients](<https://devfeed.tech/tags/quotients.md>), [spaces](<https://devfeed.tech/tags/spaces.md>), [topology](<https://devfeed.tech/tags/topology.md>)

### AI overview

This primer explains how to construct more complex topological spaces from simpler ones using subspaces and quotients. It introduces the subspace topology and defines spheres, including the circle, as topological spaces.

### Source excerpt

Last time we investigated the (very unintuitive) concept of a topological space as a set of "points" endowed with a description of which subsets are open. Now in order to actually arrive at a discussion of interesting and useful topological spaces, we need to be able to take simple topological spaces and build them up into more complex ones. This will take the form of subspaces and quotients, and through these we will make rigorous the notion of "gluing" and "building" spaces.

## Metric Spaces -- A Primer

DevFeed: [Metric Spaces -- A Primer](<https://devfeed.tech/articles/metric-spaces-a-primer-40285.md>)

Original publisher: [Read original article](<https://www.jeremykun.com/2012/08/26/metric-spaces-a-primer/>)

Published: 2012-08-26T12:08:25Z

Content type: tutorial

Language: en

Sources: [Jeremy Kun](<https://devfeed.tech/sources/jeremy-kun.md>)

Topics: [Mathematics](<https://devfeed.tech/topics/mathematics.md>), [Math and Logic](<https://devfeed.tech/topics/math-and-logic.md>), [Algorithms, Complexity](<https://devfeed.tech/topics/algorithms-complexity.md>)

Tags: [algorithms](<https://devfeed.tech/tags/algorithms.md>), [levenshtein-distance](<https://devfeed.tech/tags/levenshtein-distance.md>), [mathematics](<https://devfeed.tech/tags/mathematics.md>), [metric](<https://devfeed.tech/tags/metric.md>), [symmetry](<https://devfeed.tech/tags/symmetry.md>), [topology](<https://devfeed.tech/tags/topology.md>), [triangle-inequality](<https://devfeed.tech/tags/triangle-inequality.md>)

### AI overview

This tutorial introduces metric spaces as sets equipped with distance functions that satisfy non-negativity, symmetry, and the triangle inequality. It explains that metrics impose a topology and contrasts metric-based work with approaches using non-metrics.

### Source excerpt

The Blessing of Distance We have often mentioned the idea of a "metric" on this blog, and we briefly described a formal definition for it. Colloquially, a metric is simply the mathematical notion of a distance function, with certain well-behaved properties. Since we're now starting to cover a few more metrics (and things which are distinctly not metrics) in the context of machine learning algorithms, we find it pertinent to lay out the definition once again, discuss some implications, and explore a few basic examples.