# Questions tagged [topology]

Topology the study of objects that can be continuously deformed into other objects without tearing or making holes in the object. It can also mean a family of sets that have the property of a topological space. The properties are convergence, connectedness, and continuity.

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### Topologies for modelling divergence in the lambda-calculus

I wonder if there exist topologies for the lambda-calculus where computational divergence (like for $\Omega = (\lambda x. x x) (\lambda x. x x)$) has a topological meaning as the divergence of a ...
143 views

### Reference request: Shortest homotopic curve via vertex releases

Let $C$ be a piecewise-linear path (or closed curve) in the plane, in the presence of polygonal obstacles. We would like to find the shortest path (or curve) homotopic to $C$. (A path $D$ is homotopic ...
133 views

### Do Banach spaces and linear contraction maps form a model of ILL with an exponential?

Recently, I read on the nLab that the category of Banach spaces and linear contractions is small complete, small cocomplete, and monoidal closed. This means that Banach spaces and short linear maps ...
108 views

### Topology/Space of Recursive Algebraic Datatypes

I have a recursive algebraic datatype. I (somewhat arbitrarily) defined one function to compute distance between instances, and am trying to define a function to approximate a "vector" between ...
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### How to design an algorithm which turns an undirected graph into directed with all nodes of indegree higher than 0? [closed]

Given an undirected graph $G=(V,E)$ devise an algorithm that will check whether its edges can be directed in such a way that the vertices of the resulting directed graph will all have indegree higher ...
101 views

### Structures obtained by gluing simplices

I'm looking for the correct name of geometric structures obtained as follows. 2-structures: A collection $X$ of triangles is a $2$-structure. If $X$ is a $2$-structure and $Y$ is obtained from $X$ ...
196 views

### Applications of “Seemingly Impossible Functional Programs”

What are some practical applications (existing or potential) for Martin Escardo's "Seemingly Impossible Functional Programs"? For starters, here are a few from: Alex Simpson’s Lazy functional ...
102 views

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### Is there a geometrical picture for adiabatic quantum computation?

In adiabatic quantum computation (AQC), one encodes the solution to an optimization problem in the ground state of a [problem] Hamiltonian $H_p$. To get to this ground state, you start in an easily ...
104 views

### test if a polygon-surface is closed (+ additional nice-to-have requirements)

I have a 3D object bounded by Polygons. Is there a standard algorithm that tests if the volume is closed e.g. no polygon is missing? Example: I have a cube bounded by six squares. The algorithm ...
193 views

### Relation between vertices, cells, and vertex-cell-incidences in 3D subdivisions

Consider a planar subdivision, with F faces, V vertices, E edges, and I face-vertex incidences. For simplicity, assume a "non-degenerate" situation in which each vertex occurs on the boundary cycle of ...
Consider a set of trees $T=\{T_{\alpha}\}$, and for any $T_{\alpha}\in T$, $T_{\alpha}$ has $n$ nodes. Can we find a ‘characteristic’ function $f:T\longmapsto{\mathbb{R}}$ describing trees' ...