topological

For topological spaces with a countable (local) basis, the converse is also true.

Basically, whenever you have uncountable sets, they come along with some topological structure which must be handled continuously.

Perhaps it's a topological insulator, so that the bulk conducts but you'd never know it because the surface doesn't.

The reloaded workflow is just a pattern around building objects with a topological sort for order initialization.

It has an inside as much as any bottle does, but the only point of a Klein Bottle is the topological form so they're using topological language to talk about it.

Well, they noticed that you could add another branch to the Isomorphism: programs are points, types are topological spaces.

There is also clearly no comprehension of the importance of the topological (circuitry) defining a neural network.

A vaccuum flask is simply a deformed sphere in topological terms, and thus only has two surfaces, the inside and the outside.

This isn't just on the theory side; experimentalists are looking at topological states of matter for a variety of applications, including quantum computing.

This isn't so surprising, because category theory has always been a bit topological.

A d-dimensional manifold is a topological space with the property that all small enough bits of it look like ordinary d-dimensional Euclidean space.

For example, topological quantum field theory[1] has found widespread important applications in quantum information, and it was pioneered by none other than Witten himself.

Here functional is not intended as "functional programming" but as the closest way I found in programming to express topological concepts.

> "in this sort of a situation, one must work with the Galois groups involved as abstract topological groups, which are not equipped with the 'labeling apparatus'.

They also found that equality could be defined as the existence of a path between two points -- two objects/proofs are equal precisely when they belong to the same "lump of rubber" in a topological space.

Try translating this, from an actual textbook, to toki pona: "This section shows how depth-first search can be used to perform a topological sort of a directed acyclic graph, or a 'dag' as it is sometimes called.

Topological spaces can be pretty weird, so topologists are interested in various more restricted kinds of space that look more like the geometrical objects we're familiar with.