Begin by taking the 0-skeleton to be a discrete space.

Examples more general than those are the discrete space groups.

It follows in particular, that the fiber is a discrete space.

Thus, the different notions of discrete space are compatible with one another.

Every discrete space with at least two points is totally disconnected.

Assume that a function on a discrete space (usually a graph) is given.

The topological dimension of a discrete space is equal to 0.

Any two discrete spaces with the same cardinality are homeomorphic.

Thus, the three definitions are non-equivalent on an uncountable discrete space.

Note that is homeomorphic to the join where is a discrete space with two points.

While the studios are discrete spaces, they share existing windows and a lounge in the middle of the vertical space.

A 0-manifold is just a discrete space.

However any uncountable discrete space is first-countable but not second-countable.

These subspaces increase with n. The 0-skeleton is a discrete space, and the 1-skeleton a topological graph.

On the other hand, a discrete space is totally disconnected, so is connected only if it has at most one point.

In a uniform distribution on a discrete space, all probabilities are equal unit fractions.

X is homeomorphic to the one-point compactification of a discrete space.

A discrete space is coherent with every family of subspaces (including the empty family).

The pointed set concept is less important; it is anyway the case of a pointed discrete space.

A discrete space is compact if and only if it is finite.

Any discrete space is a 0-dimensional manifold.

Some of these include: gravitation problems, deritrinitration, theory of discrete space, etc.

In any discrete space, since every set is open, every set is equal to its interior.

Every non-empty discrete space is second category.

Another counterexample is a product of uncountably many copies of an infinite discrete space.