---
tag: CCZA91NE5X
kind: concept
name: Open segment
msc: [52A05]
sources:
  - url: https://en.wikipedia.org/wiki/Line_segment
---

## Summary

The open segment between two points is the [[line segment|VQ4Q2V45RP]] between them with the two endpoints removed, when the points are distinct.
Open segments appear in the definitions of [[extreme points|3MSGFJM2NX]], extreme sets and faces.
These notions ask what happens when a point of a set lies strictly between two other points.
They also define strict convexity of sets.

## Explanations

### L1 human

Draw the segment from $x$ to $y$ and erase its two ends.
What is left is the open segment: the points strictly between $x$ and $y$.
In coordinates these are the points $(1 - t) x + t y$ with $0 < t < 1$.
For example, the open segment from $0$ to $1$ on the real line is the open interval $(0, 1)$.