In addition, the term is used in a broader sense to cover a world-view on a wide variety of topics, including chemical evolution as an alternative term for abiogenesis or for nucleosynthesis of chemical elements, galaxy formation and evolution, stellar evolution, spiritual evolution, technological evolution and universal evolution, which seeks to explain every aspect of the world in which we live.

* The universal cover of a connected Lie group is a Lie group.

For example, the group R is the universal cover of the circle group S < sup > 1 </ sup >.

In fact any covering of a differentiable manifold is also a differentiable manifold, but by specifying universal cover, one guarantees a group structure ( compatible with its other structures ).

In Ferdydurke ( his first novel, published in autumn 1937, the date on the cover 1938 ) discusses form as a universal category which was understood both in the philosophical, sociological, and aesthetic sense.

The concept of a universal cover was first developed to define a natural domain for the analytic continuation of an analytic function.

The universal cover of SO ( 3 ) is a Lie group called Spin ( 3 ).

" popularity is based on universal rock & roll virtues ," said Rolling Stone, which put the band on the cover of its January 7, 1993 issue.

is the universal cover of SL ( 2, R ), which fibers over H < sup > 2 </ sup >.

* If π < sub > 1 </ sub >( M ) has an infinite normal cyclic subgroup but is not virtually solvable then the geometric structure on M is either H < sup > 2 </ sup >× R or the universal cover of SL ( 2, R ).

Note that this means that algebraic group is narrower than Lie group, when working over the field of real numbers: there are examples such as the universal cover of the 2 × 2 special linear group that are Lie groups, but have no faithful linear representation.

A connected covering space is a universal cover if it is simply connected.

The name universal cover comes from the following important property: if the mapping is a universal cover of the space and the mapping is any cover of the space where the covering space is connected, then there exists a covering map such that.

< BLOCKQUOTE > The universal cover of the space covers all connected covers of the space .</ BLOCKQUOTE >

If the space has a universal cover then that universal cover is essentially unique: if the mappings and are two universal covers of the space then there exists a homeomorphism such that.

If the change, at first sight, seems minor, we may recall that it took the Italian painters about two hundred years to make an analogous change, and the Italian painters, by universal consent, were the most brilliant group of geniuses any art has seen.

In modern English, " Americans " generally refers to residents of the United States, and among native speakers of English this usage is almost universal, with any other use of the term requiring specification of the subject under discussion.

Both sides ( with the exception of hyper-Calvinists ) believe the invitation of the gospel is universal and " must be presented to everyone can reach without any distinction.

" He points to the fact that the Pope claims universal jurisdiction and he therefore argues that " it would be intolerable to have, as the sovereign of a Protestant and free country, one who owes any allegiance to the head of any other state " and contends that if such situation came about " we will have undone centuries of common law.

As the title implies, any active device received the sum of all transmitted messages in universal space-time, in a single pulse, so that demultiplexing yielded information about the past, present, and future.

MSP Alex Johnstone wrote " Clearly, the Declaration of Arbroath is a literary work of outstanding universal significance by any stretch of the imagination " In 2008, the Campaign Group Chairman, Councillor Jim Millar launched a public petition to reinforce the bid explaining " We're simply asking people to, local people especially, to sign up to the campaign to have the Declaration of Arbroath and Arbroath Abbey recognised by the United Nations.

* " I foresee a universal information system ( UIS ), which will give everyone access at any given moment to the contents of any book that has ever been published or any magazine or any fact.

The tensor product X ⊗ Y from X and Y is a K-vector space Z with a bilinear function T: X × Y → Z which has the following universal property: If T ′: X × Y → Z ′ is any bilinear function into a K-vector space Z ′, then only one linear function f: Z → Z ′ with exists.

Different magazines were published featuring programs for specific computers, though some BASIC programs were considered universal and could be used in machines running any variant of BASIC ( sometimes with minor adaptations ).

The domain of any universal computable function is a computably enumerable set but never a computable set.

He conceived the idea of adding an unalterable and universal message on spacecraft destined to leave the solar system that could potentially be understood by any extraterrestrial intelligence that might find it.

There is no universal answer for how to sort such strings ; any rules are application dependent.

It has the following universal property: if N is any complete metric space and f is any uniformly continuous function from M to N, then there exists a unique uniformly continuous function f ' from M ' to N, which extends f. The space M is determined up to isometry by this property, and is called the completion of M.

Namely φ is universal for homomorphisms from G to an abelian group H: for any abelian group H and homomorphism of groups f: G → H there exists a unique homomorphism F: G < sup > ab </ sup > → H such that.

Scholars of general semantics emphasize distinctions between different perceptions at different points in space ( called " space-binding ") over any universal God's eye view or assumed-shared or collective identity.

According to Newton's law of gravity, and independently verified by experiments such as that of Eötvös and its successors ( see Eötvös experiment ), there is a universality of free fall ( also known as the weak equivalence principle, or the universal equality of inertial and passive-gravitational mass ): the trajectory of a test body in free fall depends only on its position and initial speed, but not on any of its material properties.

One of the reasons given for developing Galileo as an independent system was that position information from GPS can be made significantly inaccurate by the deliberate application of universal Selective Availability ( SA ) by the US military ; this was enabled until 2000, and can be re-enabled at any time.

But having abandoned abstract philosophical speculation in his youth, Marx himself showed great reluctance during the rest of his life about offering any generalities or universal truths about human existence or human history.

A universal hashing scheme is a randomized algorithm that selects a hashing function h among a family of such functions, in such a way that the probability of a collision of any two distinct keys is 1 / n, where n is the number of distinct hash values desired — independently of the two keys.

States and individuals who subscribe to this view opine that, in the case of the individual responsible for violation of international law, he " is become, like the pirate and the slave trader before him, hostis humani generis, an enemy of all mankind ", and thus subject to prosecution in a fair trial before any fundamentally just tribunal, through the exercise of universal jurisdiction.

Every individual is connected with the rest of the world, and the universe is fashioned for universal harmony.

Some modern hi-fi equipment can be digitally connected using fibre optic TOSLINK cables, universal serial bus ( USB ) ports ( including one to play digital audio files ), or Wi-Fi support.

Baptism is the mark of membership in the covenant of grace and in the universal church, although regeneration is not inseparably connected with baptism.

It is believed to be a field of universal knowledge and is somehow connected to the terrestrial artifact in the Global Dynamics labs.

which is natural in the variables N and F. The counit of this adjunction is simply the universal cone from lim F to F. If the index category J is connected ( and nonempty ) then the unit of the adjunction is an isomorphism so that lim is a left inverse of Δ.

The unit of this adjunction is the universal cocone from F to colim F. If J is connected ( and nonempty ) then the counit is an isomorphism, so that colim is a left inverse of Δ.

However, it can also refer to the concept of such a language being determined by international consensus, including even a standardized natural language ( e. g., International English ), and has also been connected to the project of constructing a universal language.

Other noteworthy unknots are those that consist of rigid line segments connected by universal joints at their endpoints ( linkages ), that yet cannot be reconfigured into a convex polygon, thus acquiring the name stuck unknots.

This allows a VGA monitor to be connected with a passive plug adapter and offers a universal solution for the DVI interface.

In South Wales again, where in 1811 the railways were connected with canals, collieries, iron and copper works, and had a total length of nearly, the plateway was almost universal.

For n > 2, Spin ( n ) is simply connected, and thus the universal covering group for SO ( n ).

Menger showed, in the 1926 construction, that the sponge is a universal curve, in that any possible one-dimensional curve is homeomorphic to a subset of the Menger sponge, where here a curve means any compact metric space of Lebesgue covering dimension one ; this includes trees and graphs with an arbitrary countable number of edges, vertices and closed loops, connected in arbitrary ways.

The rig is connected to the board by a free-rotating universal joint and consists of a mast, 2-sided boom and sail.

The differential is connected to the engine via a swinging drive shaft and a universal joint.

The space has a universal cover if it is connected, locally path-connected and semi-locally simply connected.