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 major failure to a spacecraft en route is likely to be fatal, and even a minor one could have dangerous results if not repaired quickly, something difficult to accomplish in open space.

Any decision in allocating capital is likewise: there is an opportunity cost of capital, or a hurdle rate, defined as the expected rate one could get by investing in similar projects on the open market.

Any legal wrestler is open to attack from any direction at any time, including when they are downed, as long as they are within the ring area enclosed by the ring ropes.

Any canal built open to all nations on equal terms.

Eric Raymond extends this principle in support of open source security software, saying, " Any security software design that doesn't assume the enemy possesses the source code is already untrustworthy ; therefore, never trust closed source.

* Any topological space can be viewed as a category by taking the open sets as objects, and a single morphism between two open sets and if and only if.

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.

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.

Any relatively flat, open space can be used as a terrain.

* Aranym Atari Running on Any Machine: an open source emulator / virtual machine that can run Atari GEM applications

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.

( 2 ) Any non-profit corporation, civic association, or governmental entity which has buildings and grounds open to the public may request for the appointment of constables to serve as law enforcement officers in order to protect life and property.

* 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 competitors desiring their names to be attached to their contributions will please give permission to the Committee to open the envelopes inscribed with their mottoes.

Any open cover of a paracompact space is numerable.

Any future attempt to recover his throne would have to be with the open support of the English king.

Any point x gives rise to a continuous function p < sub > x </ sub > from the one element topological space 1 ( all subsets of which are open ) to the space X by defining p < sub > x </ sub >( 1 ) = x. Conversely, any function from 1 to X clearly determines one point: the element that it " points " to.

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

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

Any measurable subset of a null set is itself a null set.

* 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.