/sci/ - Science & Math

>>11167209
https://en.wikipedia.org/wiki/Simplex
A 0-simplex (point) is a single vertex.
A 1-simplex (line segment) is two vertices and the line segment between them
A 2-simplex (triangle) is three vertices, the lines segments between them, and the triangle bounded by the line segments
A 3-simplex (pyramid) is four vertices, the line segments between them, the faces between the line segments, and the volume between the faces.
In general an n-simplex is like an n-dimensional triangle.

A map from an n-simplex to a space is almost like viewing the n-simplex as embedded in your space (you can imagine a triangle on the surface of a sphere for example). The place where this breaks down however is that maps can send multiple points to the same point in your space, so the embedding can be a weird, twisted, self-intersecting one.

>What do topological spaces look like, both abstractly and symbolically.
Read the Wikipedia article I linked.