In general topological spaces, however, the different notions of compactness are not necessarily equivalent, and the most useful notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, involves the existence of certain finite families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

In general topological spaces, however, the different notions of compactness are not equivalent, and the most useful notion of compactness — originally called bicompactness — involves families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

Some of these men were executed as early as 83 or 85 however, lending little credit to Tacitus ' notion of a " reign of terror " late in Domitian's reign.

One of several views of epistemology, the study of human knowledge, along with rationalism, idealism, and historicism, empiricism emphasizes the role of experience and evidence, especially sensory perception, in the formation of ideas, over the notion of innate ideas or traditions ; empiricists may argue however that traditions ( or customs ) arise due to relations of previous sense experiences.

John Elliot, however, suggests that the notion of Silvanus as secretary or author or drafter of 1 Peter represents little more than a counsel of despair and introduces more problems than it solves because the Greek rendition of 5: 12 suggests that Silvanus was not the secretary, but the courier / bearer of 1Peter.

Beginning in the late 19th and early 20th century however, policies such as Woodrow Wilson's mission to " make the world safe for democracy " were often backed by military force, but more often effected from behind the scenes, consistent with the general notion of hegemony and imperium of historical empires ..

It is, however, an unfortunately obscure and controversial notion.

This notion, however, is much more generally expressed in Latin by placere or delectāre, which are used more colloquially, the latter used frequently in the love poetry of Catullus.

Non-reductive materialism explicitly rejects this notion, however, taking the material constitution of all particulars to be consistent with the existence of real objects, properties, or phenomena not explicable in the terms canonically used for the basic material constituents.

Some scholars, however, dispute the notion that the Essenes wrote the Dead Sea Scrolls.

Influential to thinkers associated with Postmodernism are Heidegger's critique of the subject-object or sense-knowledge division implicit in Rationalism, Empiricism and Methodological Naturalism, his repudiation of the idea that facts exist outside or separately from the process of thinking and speaking them ( however, Heidegger is not specifically a Nominalist ), his related admission that the possibilities of philosophical and scientific discourse are wrapped up in the practices and expectations of a society and that concepts and fundamental constructs are the expression of a lived, historical exercise rather than simple derivations of external, apriori conditions independent from historical mind and changing experience ( see Johann Gottlieb Fichte, Heinrich von Kleist, Weltanschauung and Social Constructionism ), and his Instrumentalist and Negativist notion that Being ( and, by extension, reality ) is an action, method, tendency, possibility and question rather than a discreet, positive, identifiable state, answer or entity ( see also Process Philosophy, Dynamism, Instrumentalism, Pragmatism and Vitalism ).

This notion however is a superficial comprehension, prompted no doubt by Breton's initial emphasis on automatic writing as the main route toward a higher reality.

At the same time, however, and owing to both the presence of another prominent sociologist at the Institute, Karl Mannheim, as well as the methodological problem posed by treating objects-like " musical material "-as ciphers of social contradictions, Adorno was compelled to abandon any notion of " value-free " sociology in favor of a form of ideology critique which held on to an idea of truth.

The other states, however, did not follow suit and several rejected the notion that states could nullify federal law.

Present-day common use, however, often restricts the notion to the present part of North Rhine-Westphalia.

The notion of such an action by an audience was however recognized in antiquity, as seen particularly in the Roman theoretical concerns of Horace, who also lived in an age of increasing skepticism about the supernatural, in his Ars Poetica.

The notion of exclusivity however is challenged by the existence of similar forces working against different social and ethnic groups such as homosexuals and the Roma, which resulted in the victimization and systematic destruction of homosexual lives and lifestyles, as well as those of the Roma.

The smallest constant is sometimes called the ( best ) Lipschitz constant ; however in most cases the latter notion is less relevant.

There is, however, no Orthodox notion equivalent to the papacy: the Orthodox churches operate in the synodical system, whereby ecclesiastical matters are settled by the competent synod of bishops, in which each bishop has one vote.

The same text, however, also exempts religious sacrifice from the notion of " violence " since the victim of the sacrifice was taken to benefit from the act as it would be reborn in a higher position.

Catherine did not like this notion, however.

The notion of an explicit exception française however has angered many of France's critics.

In geometry, a hyperplane of an n-dimensional space V is a " flat " subset of dimension n − 1, or equivalently, of codimension 1 in V ; it may therefore be referred to as an ( n − 1 )- flat of V. The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly ; in all cases however, any hyperplane can be given in coordinates as the solution of a single ( due to the " codimension 1 " constraint ) algebraic equation of degree 1 ( due to the " flat " constraint ).

Despite these assertions, however, it is largely recognized and accepted by practitioners and researchers that leadership is important, and research supports the notion that leaders do contribute to key organizational outcomes ( Day & Lord, 1988 ; Kaiser, Hogan, & Craig, 2008 ).

We have staved off a war and, since our behavior has involved all these elements, we can only keep adding to our ritual without daring to abandon any part of it, since we have not the slightest notion which parts are effective.

In she has it in for George dominant stress will ordinarily be on in, where the notion of stored-up antipathy seems to center.

The notion of philosophy as Queen Bee may fit well with authoritarian modes of political ideology, but it has been noted that the price of such an imperial notion of philosophy is the frustration and flagellation of the social sciences.

The threadbare notion that belief, unlike behaviour, is not subject to objective analysis, has placed intuitive metaphysics squarely against the sociology of knowledge, since it is precisely the job of the sociology of knowledge to treat beliefs as social facts no less viable than social behaviour.

In such a case, any attitude would be as fitting or unfitting as any other, which means that the notion of fitness has lost all point.

And Mityukh, apparently the intellectual leader of the crowd, replies that he has no notion.

( Pp. 228-229 ) in any event, it is obvious that the anti-trust laws did not prevent the formation of some of the greatest financial empires the world has ever known, held together by some of the most fantastic ideas, all based on the fundamental notion that a corporation is an individual who can trade and exchange goods without control by the government ''.

John C. Cavadini has challenged this notion by attempting to take the Spanish Christology in its own Spanish / North African context in his important study, The Last Christology of the West: Adoptionism in Spain and Gaul, 785 – 820.

So broad a notion has inevitably been elusive and controversial in the history of philosophy, beginning in western philosophy with attempts among the pre-Socratics to deploy it intelligibly.

The notion that the Third Reich developed a blitzkrieg strategy to achieve its total aims has been widely attacked.

The widely accepted notion that the security of the system should depend on the key alone has been explicitly formulated by Auguste Kerckhoffs ( in the 1880s ) and Claude Shannon ( in the 1940s ); the statements are known as Kerckhoffs ' principle and Shannon's Maxim respectively.

In light of this, and the practical difficulty of managing such long keys, modern cryptographic practice has discarded the notion of perfect secrecy as a requirement for encryption, and instead focuses on computational security, under which the computational requirements of breaking an encrypted text must be infeasible for an attacker.

The Whig-liberal tradition has led to the well-known notion of ( negative ) freedom as lack of specific coercion.

For example, it has been suggested that, in the early 20th century Shanghai, “ Western food, and in particular identifiably nourishing items like milk, became a symbol of a neo-traditional Chinese notion of family .”

It may be a cultural notion, but has very little weight in international discourse ; very few political observers really discuss Christendom, while the Muslim World tends to comprise of a civilization in itself.

" Christendom " has referred to the medieval and renaissance notion of the Christian world as a sociopolitical polity.

The Council of Chalcedon issued the ' Chalcedonian Definition ,' which repudiated the notion of a single nature in Christ, and defined that he has two natures in one person and hypostasis ; it also insisted on the completeness of his two natures: Godhead and manhood.

However, Judeo-Christian thought also makes an " innovation of the first importance ", Eliade says, because it embraces the notion of linear, historical time ; in Christianity, " time is no longer the circular Time of the Eternal Return ; it has become linear and irreversible Time ".

Kant's notion of critique has been associated with the disestablishment of false, unprovable, or dogmatic philosophical, social, and political beliefs, because Kant's critique of reason involved the critique of dogmatic theological and metaphysical ideas and was intertwined with the enhancement of ethical autonomy and the Enlightenment critique of superstition and irrational authority.

The notion of definability treated in this article has been chosen primarily for definiteness, not on the grounds that it's more useful or interesting than other notions.

This understanding has led to the notion that all the information needed for proteins to assume their native state was encoded in the primary structure of the protein, and hence in the DNA that codes for the protein, the so called " Anfinsen's thermodynamic hypothesis ".

" Even today, though these errors have been recognized for more than a century, the general notion that Lao Tzu was Christ's forerunner has lost none of its romantic appeal.

He has also written about and advocated the notion of memetics as a philosophically useful tool, most recently in his " Brains, Computers, and Minds ", a three part presentation through Harvard's MBB 2009 Distinguished Lecture Series.

Although modern historians have rejected this hypothesis, Czech historiography has supported the notion of mixed Piast-Přemyslid parentage for Vladivoj.