* Any finite topological space, including the empty set, is compact.

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

* Any two finite fields with the same number of elements are isomorphic.

# Any finite straight line can be extended in a straight line.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

Any meaningful theory of quantum gravity that makes sense and is predictive at all energy scales must have some deep principle that reduces the infinitely many unknown parameters to a finite number that can then be measured.

Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

Any digital modulation scheme uses a finite number of distinct signals to represent digital data.

Any finite product in a preadditive category must also be a coproduct, and conversely.

Any finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover.

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.

Any finite extension of a finite field is a cyclic extension.

Any structure implicit in the finite entropy against a quantum description could then be totally washed out by the huge injection of uncertainty this projection represents.

Any Calabi – Yau manifold has a finite cover that is the product of a torus and a simply-connected Calabi – Yau manifold.

Any finite simplicial complex in the sense talked about here can be embedded as a polytope in that sense, in some large number of dimensions.

Any Fredholm operator has an index, defined as the difference between the ( finite ) dimension of the kernel of D ( solutions of Df = 0 ), and the ( finite ) dimension of the cokernel of D ( the constraints on the right-hand-side of an inhomogeneous equation like Df

* Any category with finite products is monoidal with the product as the monoidal product and the terminal object as the unit.

Any alteration of one of these factors is distortion, although we generally use that word only for effects so pronounced that they can be stated quantitatively on the basis of standard tests.

Any word or phrase that exactly reproduces the letters in another order is an anagram.

Any suggestion I may have made to you will be without force when I say the word ' cancelled.

Alfred Korzybski criticized the use of the verb " to be ", and stated that, " Any proposition containing the word ' is ' its other forms ' are ,' ' be ', etc.

Any symbol or word which does not violate the rules of the language can be used as a metasyntactic variable, but nonsense words are commonly used.

Any word combination that corresponds to a complete subtree can be seen as a phrase.

Any word or any combination of words that are linked together by dependencies qualifies as a catena.

:" Any person who, on or in connection with any goods or services, or any container for goods, uses in commerce any word, term, name, symbol, or device, or any combination thereof, or any false designation of origin, false or misleading description of fact, or false or misleading representation of fact, which

Any chamber used as a burial place is a catacomb, although the word is most commonly associated with the Roman empire.

Any object so sacrificed or devoted to the Lord could not be redeemed (; ); and hence the idea of exterminating was connected with the word.

Any player may challenge the validity of a word, in which case a previously nominated dictionary is used to verify or refute it.

Any other use of the word is considered improper both linguistically and technically.

Any member who by word or action showed that his principles were contrary to the constitution and the rights of man was to be expelled, a rule which later on facilitated the " purification " of the society by the expulsion of its more moderate elements.

* Any raptor which has the word buzzard as part of its name.

This view received strong support from the press ; The Times wrote, " The Old Vic began by offering opera of some sort to people who hardly knew what the word meant ... under a wise, fostering guidance it has gradually worked upwards ... Any kind of amalgamation which made it the poor relation of the ' Grand ' season would be disastrous.

** Any type of cereals or edible grains ( much like the English corn ), but this use of the word is becoming increasingly obsolete

Any spoken word or words can be a voice tag, and can be used to dial a contact or in some cases, open an application.

Any element can be expressed as a word in the T-alphabet

Any word or instance of communication that has its effectiveness reduced due to semantic discord is said to be semantically loaded.

Any of the addressing modes mentioned in this article could have an extra bit to indicate indirect addressing, i. e. the address calculated using some mode is in fact the address of a location ( typically a complete word ) which contains the actual effective address.

Any English sentence can be composed from a small vocabulary, such as the word set of Basic English.

* Any word that begins with an " f "

Any team member could also pass as often as possible to throw out the current word.

Any prefix of the specific Fibonacci word belongs to L, but so do many other strings.