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Algebraic topology is the study of intrinsic qualitative aspects of spatial objects (e.g., surfaces, spheres, tori, circles, knots, links, configuration spaces, etc.) that ...

Fuglede (1974) conjectured that a domain Omega admits an operator spectrum iff it is possible to tile R^d by a family of translates of Omega. Fuglede proved the conjecture in ...

A hyper-Kähler manifold can be defined as a Riemannian manifold of dimension 4n with three covariantly constant orthogonal automorphisms I, J, K of the tangent bundle which ...

An International Standard Book Number (ISBN) is a code used to uniquely identify a book together. It also uniquely encodes the book's publisher and includes information about ...

Let three equal circles with centers J_A, J_B, and J_C intersect in a single point H and intersect pairwise in the points A, B, and C. Then the circumcircle O of the ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

Abstract algebra is the set of advanced topics of algebra that deal with abstract algebraic structures rather than the usual number systems. The most important of these ...

In the algebraic geometry of Grothendieck, a stack refers to a sheaf of categories. In particular, a stack is a presheaf of categories in which the following descent ...

An aperiodic monotile, also somewhat humorously known as an einstein (where "einstein" means "one stone", perhaps generalizable to "one tile," in German), is a single tile ...

Baer's criterion, also known as Baer's test, states that a module M over a unit ring R is injective iff every module homomorphism from an ideal of R to M can be extended to a ...