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Page "Meagre set" ¶ 10
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Any and subset
Any subset of B is also well-ordered.
:* Any subset of the identity relation on X has equivalence classes that are the singletons of X.
Any subset of R < sup > n </ sup > ( with its subspace topology ) that is homeomorphic to another open subset of R < sup > n </ sup > is itself open.
Any one language has only a subset of the aspectual distinctions attested in the world's languages, and some languages ( such as Standard German ; see below ) do not have aspects.
Any measurable subset of a null set is itself a null set.
Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.
Any second-countable space is separable: if is a countable base, choosing any gives a countable dense subset.
Any subset of resource, but typically at least the processor state, may be associated with each of the process ' threads in operating systems that support threads or ' daughter ' processes.
Any function can be restricted to a subset of its domain.
* Any open subset of a finite-dimensional real, and therefore complex, vector space is a diffeological space.
Any ordinal is, of course, an open subset of any further ordinal.
Any discrete subset of Euclidean space is countable, since the isolation of each of its points ( together with the fact the rationals are dense in the reals ) means that it may be mapped 1-1 to a set of points with rational co-ordinates, of which there are only countably many.
Any proposed inverse R of F ( reconstruction formula, in the lingo ) would have to map to some subset of.
Any action of the group by continuous affine transformations on a compact convex subset of a ( separable ) locally convex topological vector space has a fixed point.
Any induced subgraph of a comparability graph is itself a comparability graph, formed from the restriction of the partial order to a subset of its elements.
* Any directed set A may be made into a Cauchy space by declaring a filter F to be Cauchy if, given any element n of A, there is an element U of F such that U is either a singleton or a subset of the tail
Any subset of a group closed under multiplication, under inversion and under identity ( i. e.
Any given neuron only responds to a subset of stimuli within its receptive field.
* Any open subset of an n-manifold is a n-manifold with the subspace topology.
Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

Any and set
Any such totality would itself have to be a set, thus lying somewhere within the hierarchy and thus failing to contain every set.
* Any finite topological space, including the empty set, is compact.
Any definition that attempts to set out the essence of something, such as that by genus and differentia, is an intensional definition.
Any consistent set of units may be used, although SI units are preferred.
* Any singleton set
Any regional variety of English has a set of political, social and cultural connotations attached to it, even the so-called ' standard ' forms.
Any partially ordered set I can be considered as a small category where the morphisms consist of arrows i → j if and only if i ≤ j.
: Premise: Any cognitive state occurs as part of a set of cognitive states and within a cognitive system
* Extensibility: Any database system has its own predefined set of data types which we can use to build new types ( see Complex Objects ), but a purely extensible system is designed such that there are no logical differences between built-in ( or ' primitive ') data types and ' custom ' data types, though there may be strong differences in the way the two are implemented.
Any slight initial imbalance between taste and tails may set off an explosion in tail lengths.
Any byte with the high bit set was a special Telnet character.
* Any attempt to set up a telecommunication circuit
Any given instruction set can be implemented in a variety of ways.
Any discussion of Muslim magic poses a double set of problems.
Any other cogenerator ( or cogenerating set ) can be used in this construction.
Any preordered set ( P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y.
Any ordinal number can be seen as a category when viewed as an ordered set.
Any given animal uses a relatively restricted set of gaits, and different species use different gaits.
Any statement that has a Y following the command letter is processed only if the match flag is set.
Any collection of subsets of a set X satisfying these properties forms a base for the closed sets of a topology on X.
* Any partially ordered set can be interpreted as a category: the objects are the elements of, and there is a single morphism from to if and only if.
Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.

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