* 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.

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 contiguous subsequence of a word

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 street meeting, sacred or secular, which he and his colleagues uneasily cover has as its explicit or implicit burden the cruelty and injustice of the white domination.

Any given bookmaker will weight their odds so that no one customer can cover all outcomes at a profit against their books.

Any sufficiently large-3000 members or more-youth organization organized in a democratic manner is eligible to receive government funding to cover operating expenses.

Walker sang on a rare Donovan's Brain track, " 22 Lost Marbles " ( which appeared on A Pot By Any Other Name, a free CD with issue 30 ( Spring 2001 ) of the independent music magazine Ptolemaic Terrascope ), and a Brain cover of a song " The Single # 2 ", originally by the band Man.

Songs on this album include " Any Means Necessary ", " Life is Now ", " Punish and Enslave ", " Bring the Hammer Down ", and a My Sharona cover.

Any open cover of a paracompact space is numerable.

Any given open cover of the unit circle will have a refinement consisting of a collection of open arcs.

Any player pocketing the queen is required to cover it by pocketing a carrom man of his / her chosen color.

His novel Babylon (" Generation П " or " Generation P " is the Russian title ) bears on its cover the inscription, " Any thought that occurs in the process of reading this book is subject to copyright.

It began to brag on its cover that it had " The Largest Circulation of Any Screen Magazine ", and Jean Harlow is seen reading a copy of Modern Screen in the 1933 film Dinner at Eight.

Any risk where the potential loss is so large that no one could afford to pay the market premium required to provide cover would not be commercially insurable.

Any material with varying degrees of opacity may be used, as preferred, to cover and / or obscure the desired area for burning or dodging.

Although the band had signed to Infernal Records, and their cover of God of Thunder featured on the label's Any Colour As Long As It's Black sampler, the album was never released on the label.

* Features: Any cover stories or featured games / issues that warrant a separate article would be told here.

Any sheet of material used to cover a flat or low-pitched roof is usually known as a membrane and the primary purpose of these membranes is to waterproof the roof area.

Any child being treated for pediatric cancer at Penn State Hershey is eligible for support, and the fund's policy is to fully cover all medical costs not paid by insurance.

Her cover of the Bob Dylan song " All I Really Wanna Do " was included on the Party Of Five soundtrack (' 96 ), and her compositions can also be heard in films including According to Spencer (" Something Else "), Forces of Nature (" A Rose By Any Other Name ") and The Price of Kissing (" Scandinavian Ladies ").

* Any official report of Parliament or the Privy Council, which in the 19th and early 20th centuries were standardly issued in a dark blue paper cover

Any blanket may be supplemented with a neck cover or a full hood.

Any animal in the zoo can be " adopted " for a price of US $ 100 annually to cover the cost of food and care ; the adopting party will receive a certificate and has his or her name engraved on the plaque next to the exhibit in question.

Any polyphonic instrument must use an algorithm to assign available voices to played notes ( unless the instrument has enough voices to cover all of the notes ).

Any amount of money protected by this type of cover is virtually impossible to tamper with, except the terms with which the insurance was drawn permits for such.