Indiscrete topology

Example

Let $X$ be a set and let $\tau = \{\varnothing, X\}$. Then $\tau$ is a topology 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. In an indiscrete space, each sequence converges to each point. Thus, if $X$ has at least two points, the space is not Hausdorff and not metrizable. Each indiscrete space is compact and connected.

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.