# 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.