Is a wireframe mesh like this a topology? You often see in computer

A space is not a topology. You put a topology on a space.

>>8949327
Wouldn't the rabbit be the space, and the wireframe mesh be the topology?

>>8949325
Mesh is a example of Topology.

Many sets of connected points (aka Graphs) are also a example of Topology.

But there are many other objects that can be mathematically modeled as a topology or considered a topology.

>>8949339
So if you look at the 3 axioms for something to be a topology, you have

1. The topology contains the empty set
2. The topology contains any intersections of sets in the topology
3. The topology contains any union of sets in the topology.

How does a polygonal mesh satisfy the third condition?

>>8949339

a mesh is a graph. a graph is an ordered pair of a set of vertices and a set of edges between the vertices.

Therefore the mesh is not a topology because a graph does not contain the empty set as an element.

So no, you're wrong. a mesh is not a topology you fucking retard.

>>8949329
That depends. Is the "rabbit" just the points that are also on the wireframe?

A topology is determined by whatever subsets you are calling "open." What are the open sets supposed to be here?

>>8949349
Why do people use the term "topology" so often when describing a mesh in computer graphics? Does the term just mean "connectivity" to them?

>>8949351
By "rabbit" I mean the vertices, we can them points x_i. A mesh is a bunch of sets of connected vertices {x_i,x_j}.

For this to be a topology, the union of {x_i,x_j} and {x'_i,x'_j} needs to also lie in the topology, but clearly the wireframe doesn't have any structure that indicates that.

>>8949343
>https://en.wikipedia.org/wiki/Topological_graph_theory
>Topological graph theory is a branch of graph theory. It studies the embedding of graphs in surfaces, spatial embeddings of graphs, and graphs as topological spaces.

A Mesh can be represented by a graph
Graphs can be treated as topologies, because Graphs satisfy the axioms.
So I think that Mesh can be considered topologies.

Topology in 3d modeling has no relation to the mathematical concept, by a nice topology they mean a mesh with nice properties for rendering and manipulating it.

>>8949396
Graphs can be treated as topological spaces, not topologies.

>>8949329
The natural way to look at this is the rabbit is one topological space and the mesh is its triangulation, which is basically a topological space made by gluing triangles together that is homeomorphic (topologically equivalence) to the rabbit.

>>8949425
>triangles together that is homeomorphic (topologically equivalence) to the rabbit.
wut
wouldn't the more natural interpretation be that the mesh is a simplicial complex, the rabbit is the result of applying a homeomorphism to the underlying polytope, and rabbit animations are homotopies?

>>8949425
>topological spaces, not topologies.

I think you have that backwards. Topological spaces have to satisfy the three axioms listed above.