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The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

A clear-cut way of describing every object in a class in a one-to-one manner.

A function f mapping a set X->X/R (X modulo R), where R is an equivalence relation in X, is called a canonical map.

The points on a line can be put into a one-to-one correspondence with the real numbers.

omega^epsilon=epsilon, where omega is an ordinal number and epsilon is an inaccessible cardinal.

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0, where a>0, b>a^2. The curve ...

A function f is Carathéodory differentiable at a if there exists a function phi which is continuous at a such that f(x)-f(a)=phi(x)(x-a). Every function which is Carathéodory ...

Each point in the convex hull of a set S in R^n is in the convex combination of n+1 or fewer points of S.

If Omega_1 and Omega_2 are bounded domains, partialOmega_1, partialOmega_2 are Jordan curves, and phi:Omega_1->Omega_2 is a conformal mapping, then phi (respectively, ...