* The complement of a closed nowhere dense set is a dense open set, and thus the complement of a nowhere dense set is a set with dense interior.

More precisely, the complement of a nowhere dense set is a set with dense interior.

Dually, just as the complement of a nowhere dense set need not be open, but has a dense interior ( contains a dense open set ), a comeagre set need not be a G < sub > δ </ sub > set ( countable intersection of open sets ), but contains a dense G < sub > δ </ sub > set formed from dense open sets.

In general, if E is any subset of a topological space X such that both E and the complement of E are dense in X, then the real-valued function which takes the value 1 on E and 0 on the complement of E will be nowhere continuous.

A dark roux, with its strong ( dense ) nutty flavor will completely overpower a simple seafood gumbo, but is the perfect complement to a gumbo using chicken, sausage, crawfish or alligator.

Dually, a comeagre set is one whose complement is meagre, or equivalently, the intersection of countably many sets with dense interiors.

One can also say that the diagonalizable matrices form a dense subset with respect to the Zariski topology: the complement lies inside the set where the discriminant of the characteristic polynomial vanishes, which is a hypersurface.

When a specific allophone ( from a set of allophones that correspond to a phoneme ) must be selected in a given context ( i. e. using a different allophone for a phoneme will cause confusion or make the speaker sound non-native ), the allophones are said to be complementary ( i. e. the allophones complement each other, and one is not used in a situation where the usage of another is standard ).

Altdorfer's figures are invariably the complement of his romantic landscapes ; for them he borrowed Albrecht Dürer's inventive iconography, but the panoramic setting is personal and has nothing to do with the fantasy landscapes of the Netherlands A Susanna in the Bath and the Stoning of the Elders ( 1526 ) set outside an Italianate skyscraper of a palace shows his interest in architecture.

The instruction set and register complement were highly orthogonal, making the 6809 easier to program than the 6800 or 6502.

In set theory also we have the negation operation of the complement which obeys this property: a set A and a set ( A < sup > C </ sup >)< sup > C </ sup > ( where A < sup > C </ sup > represents the complement of A ) are the same.

* Support: the smallest closed interval / set whose complement has probability zero.

Given an element φ of H *, the orthogonal complement of the kernel of φ is a one-dimensional subspace of H. Take a non-zero element z in that subspace, and set.

The definition is that a σ-algebra over a set is a nonempty collection of subsets of ( including itself ) that is closed under the complement and countable unions of its members.

They are closed under operations that one would expect for measurable sets, that is, the complement of a measurable set is a measurable set and the countable union of measurable sets is a measurable set.

Equivalently, the boundary of a set is the intersection of its closure with the closure of its complement.

Every open subgroup H is also closed, since the complement of H is the open set given by the union of open sets gH for g in G

In mathematics, a Borel set is any set in a topological space that can be formed from open sets ( or, equivalently, from closed sets ) through the operations of countable union, countable intersection, and relative complement.

A set with full measure is one whose complement is of measure zero.

In geometry, topology, and related branches of mathematics, a closed set is a set whose complement is an open set.

External aid can be effective only if it is a complement to self-help.

Dominant stress is on her luggage both in that's her luggage, where her luggage is the complement, and in there's her luggage, where it is the subject.

Mack's the leader at camp, but Jack's here, with this is deprived of stress, makes here the complement in the clause.

when it represents only itself and on which is its complement ( so that go on is semantically equivalent to board ), on has stronger stress than go does.

In the first of these sentences if by is the complement of come and Tuesday is an adjunct of time equivalent to on Tuesday, there will be strong stress on by in the spoken language ; ;

but if a complement for come is implied and by Tuesday is a prepositional unit used as an adjunct, by will be unstressed or lightly stressed at most.

In the Steiners have busy lives without visiting relatives only context can indicate whether visiting relatives is equivalent in meaning to paying visits to relatives or to relatives who are visiting them, and in I looked up the number and I looked up the chimney only the meanings of number and chimney make it clear that up is syntactically a second complement in the first sentence and a preposition followed by its object in the second.

Compared to other grains, amaranth is unusually rich in the essential amino acid lysine Common grains such as wheat and corn are comparatively rich in amino acids that amaranth lacks ; thus, amaranth and other grains can complement each other.

The term ' complementary medicine ' is primarily used to describe practices employed in conjunction with or to complement conventional medical treatments.

In linguistics, a copula ( plural: copulas or copulae ) is a word used to link the subject of a sentence with a predicate ( a subject complement ).

Costume jewelry ( also called trinkets, fashion jewelry, junk jewelry, fake jewelry, or fallalery ) is jewelry manufactured as ornamentation to complement a particular fashionable costume or garment.

Costume jewelry is meant to complement a particular fashionable garment or " costume "; Hence the name, " costume jewelry ".

In long-term psychoses, CBT is used to complement medication and is adapted to meet individual needs.

A problem is a member of co-NP if and only if its complement is in the complexity class NP.

In addition, the FDP endorses to complement the social welfare and health care systems with laws that would require every employed citizen to invest in a private social security account.

* The class of computable functions that return 0 for every input, and its complement.

ENIAC had twenty ten-digit signed accumulators which used ten's complement representation and could perform 5, 000 simple addition or subtraction operations between any of them and a source ( e. g., another accumulator, or a constant transmitter ) every second.

Conventional " full complement " chain has one tooth for every two drive links.

Another class of related results concerns perfect graphs: every bipartite graph, the complement of every bipartite graph, the line graph of every bipartite graph, and the complement of the line graph of every bipartite graph, are all perfect.

An-bit two's-complement numeral system can represent every integer in the range −( 2 < sup >− 1 </ sup >) to +( 2 < sup >− 1 </ sup > − 1 ) while ones ' complement can only represent integers in the range −( 2 < sup >− 1 </ sup > − 1 ) to +( 2 < sup >− 1 </ sup > − 1 ).

A family F of graphs is said to be closed under the operation of taking minors if every minor of a graph in F also belongs to F. If F is a minor-closed family, then let S be the set of graphs that are not in F ( the complement of F ).

The cofinite topology ( sometimes called the finite complement topology ) is a topology which can be defined on every set X.

* A semisimple operator ( or matrix ) is one for which every invariant subspace has an invariant complement.

It focuses on the female contribution to the Star Trek universe, featuring women on every card image, and a complement of female-only personnel.

* Simple set, a subset of the natural numbers that is co-infinite and recursively enumerable, but for which every infinite subset of its complement fails to be enumerated recursively.

* A Boolean algebra is a distributive lattice with least element 0 and greatest element 1, in which every element x has a complement ¬ x, such that x ∧ ¬ x

This joint venture has made every one of the company ’ s 400-plus national branch network a banking location to complement its strong Internet focus.

The opposite of a clique is an independent set, in the sense that every clique corresponds to an independent set in the complement graph.

* Ramsey's theorem states that every graph or its complement graph contains a clique with at least a logarithmic number of vertices.

# BPS does not have a preconceived phrasal structure, while in X-Bar Theory, every phrase has a specifier, a head, and a complement.

These are used to produce function definitions of every function which the users will require of the system, entity life-histories ( ELHs ) and effect correspondence diagrams, these are models of how each event interacts with the system, a complement to entity life-histories.