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There are two important theorems known as Herbrand's theorem. The first arises in ring theory. Let an ideal class be in A if it contains an ideal whose lth power is ...

A continuum is hereditarily decomposable if each of its subcontinua is decomposable. An interval is hereditarily decomposable, as is a circle, whereas the buckethandle (also ...

Let X be a continuum (i.e., a compact connected metric space). Then X is hereditarily unicoherent provided that every subcontinuum of X is unicoherent. Any hereditarily ...

Let A be a C^*-algebra. A C^*-subalgebra (that is a closed *-subalgebra) B of A is called hereditary if bab^' in B for all b,b^' in B and a in A, or equivalently if for a in ...

A property that passes from a topological space to every subspace with respect to the relative topology. Examples are first and second countability, metrizability, the ...

The representation of a number as a sum of powers of a base b, followed by expression of each of the exponents as a sum of powers of b, etc., until the process stops. For ...

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.

An optical illusion due to the physiologist Ewald Hering in 1861. The two horizontal lines are both straight, but they look as if they were bowed outwards. The distortion is ...

The illusion in view by staring at the small black dot for a half minute or so, then switching to the white dot. The black squares appear stationary when staring at the white ...

A symbol used to represent the point and space groups (e.g., 2/m3^_). Some symbols have abbreviated form. The equivalence between Hermann-Mauguin symbols (a.k.a. ...