IDs 200-299

Any open set has more than one point.

$\{x\}$ is a finite neighborhood of $x$.

In particular, singletons are discrete.

Compact sets are countably compact.

Globally implies locally.

This is just “Has a countable $k$-network $\implies$ Has a $\sigma$-locally finite $k$-network” (T352) with $T_3$ added.

$\mathcal{P}(X) = \{\emptyset, X\}$ if and only if it has 0 or 1 point.

There’s only one possible topology.

There’s only one possible topology.

If you have an infinite amount of apples, then you have at least 2 apples.

Some point has a neighborhood not containing another point.

A space is a subspace of itself.

Singletons form a network.

Every metric is a pseudometric.

Globally implies locally.

A countable basis is a local basis for every point.

$T_2$ is $T_0$ with $R_1$.

Any two distinct points are distinguishable in a $T_0$ space.

Important result to solve the Riemann hypothesis.

It has finitely many self-maps (continuous or not).