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An iterated fibration of Eilenberg-Mac lane spaces. Every topological space has this homotopy type.

Gauss's theorema egregium states that the Gaussian curvature of a surface embedded in three-space may be understood intrinsically to that surface. "Residents" of the surface ...

Oriented spheres in complex Euclidean three-space can be represented as lines in complex projective three-space ("Lie correspondence"), and the spheres may be thought of as ...

A function representable as a generalized Fourier series. Let R be a metric space with metric rho(x,y). Following Bohr (1947), a continuous function x(t) for (-infty<t<infty) ...

The Kubo-Martin-Schwinger (KMS) condition is a kind of boundary-value condition which naturally emerges in quantum statistical mechanics and related areas. Given a quantum ...

A property that passes from a topological space to all its quotient spaces. This is true for connectedness, local connectedness and separability, but not for any of the ...

A curvature of a submanifold of a manifold which depends on its particular embedding. Examples of extrinsic curvature include the curvature and torsion of curves in ...

If the section function of a centered convex body in n-dimensional Euclidean space (n>=3) is smaller than that of another such body, is its volume also smaller? The solution ...

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.

A normed vector space X=(X,||·||_X) is said to be uniformly convex if for sequences {x_n}={x_n}_(n=1)^infty, {y_n}={y_n}_(n=1)^infty, the assumptions ||x_n||_X<=1, ...