---
tag: 0XJ02JBD6S
kind: example
name: Indiscrete topology
aliases: [trivial-topology]
msc: [54A05]
instance_of: [0CQHFPGJ45]
sources:
  - url: https://en.wikipedia.org/wiki/Trivial_topology
    locator: lead section
  - url: https://en.wikipedia.org/wiki/Trivial_topology
    locator: Details
same_as:
  wikidata: Q1418327
  wikipedia: Trivial topology
---

## Example

Let $X$ be a set and let $\tau = \{\varnothing, X\}$.
Then $\tau$ is a [[topology|0CNQXVBHCX]] on $X$, the indiscrete topology, also called the trivial topology.

## Remarks

It is the coarsest topology on $X$.
Each function from any topological space to an indiscrete space is [[continuous|0SY9ECQ19Q]].
In an indiscrete space, each sequence converges to each point. Thus, if $X$ has at least two points, the space is not [[Hausdorff|0MXB4CKHFW]] and not [[metrizable|09KDHB82SG]].
Each indiscrete space is [[compact|0QPHW703PV]] and [[connected|0D939CMME7]].

## Explanations

### L1 human

In the indiscrete topology, the only open sets are the empty set and the whole space.
The topology cannot tell any two points apart.