** Hausdorff maximal principle: In any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

# REDIRECT Hausdorff maximal principle

In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 ( Moore 1982: 168 ).

The Hausdorff maximal principle is one of many statements equivalent to the axiom of choice over Zermelo – Fraenkel set theory.

The Hausdorff maximal principle states that, in any partially ordered set, every totally ordered subset is contained in a maximal totally ordered subset.

The proof that the Hausdorff maximal principle is equivalent to Zorn's lemma is very similar to this proof.

es: Principio maximal de Hausdorff

Spec ( R ) is a compact space, but almost never Hausdorff: in fact, the maximal ideals in R are precisely the closed points in this topology.

Under this duality, every compact Hausdorff space is associated with the algebra of continuous complex-valued functions on, and every commutative C *- algebra is associated with the space of its maximal ideals.

* Hausdorff maximal principle, a concept in mathematics

# REDIRECT Hausdorff maximal principle

The principle is also called the Hausdorff maximality theorem or the Kuratowski lemma ( Kelley 1955: 33 ).

The restricted principle " Every partially ordered set has a maximal totally ordered subset " is also equivalent to AC over ZF.

** Antichain principle: Every partially ordered set has a maximal antichain.

The maximal set produced by the principle is not unique, in general ; there may be many maximal totally ordered subsets containing a given totally ordered subset.

An equivalent form of the principle is that in every partially ordered set there exists a maximal totally ordered subset.

The holographic principle was inspired by black hole thermodynamics, which implies that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected.

The principle states that systems found in the natural world can perform computations up to a maximal (" universal ") level of computational power.

The fact that the black hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound ( wherein the Bekenstein bound becomes an equality ) was the main observation that led to the holographic principle.

The fact that the black hole entropy is also the maximal entropy that can be obtained by the Bekenstein bound ( wherein the Bekenstein bound becomes an equality ) was the main observation that led to the holographic principle.

These include Stein interpolation ( a variable-parameter version of complex interpolation ), the Stein maximal principle ( showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of

C syntax makes use of the maximal munch principle.

According to the principle of PECs, the two basic requirements for materials used as photo-electrodes are optical function, required to obtain maximal absorption of solar energy, and catalytic function, required for other reactions such as water decomposition.

* Initiative versus principle ; If Israel rejects the best Arab position, perhaps the Arabs should revert to maximal demands and ask Israel to propose a plan, 29 March 2007, Al-Ahram Weekly