As a rule of thumb, any sort of construction that takes as input a fairly general object ( often of an algebraic, or topological-algebraic nature ) and outputs a compact space is likely to use Tychonoff: e. g., the Gelfand space of maximal ideals of a commutative C * algebra, the Stone space of maximal ideals of a Boolean algebra, and the Berkovich spectrum of a commutative Banach ring.

The other sort of algebraic data type mentioned, " discriminated unions " ( type-safe versions of C unions ), can be defined to hold a value of any of a pre-defined type.

This means that the simple process of ' lifting ' a piece of string off itself, by the ' obvious ' use of the cross-over at a double point, is not essentially misleading: all the singularities of algebraic geometry can be recovered as some sort of very general collapse ( through multiple processes ).

Chevalley constructed a Chevalley basis ( a sort of integral form ) for all the complex simple Lie algebras ( or rather of their universal enveloping algebras ), which can be used to define the corresponding algebraic groups over the integers.

For this second sort of modules, an algebraic net formalism has been adopted.

( Note that the von Neumann algebra crossed product is usually larger than the algebraic crossed product discussed above ; in fact it is some sort of completion of the algebraic crossed product.

The effect of Gothic fiction feeds on a pleasing sort of terror, an extension of Romantic literary pleasures that were relatively new at the time of Walpole's novel.

Extension also plays an important part in the philosophy of Baruch Spinoza, who says that substance ( that which has extension ) can be limited only by substance of the same sort, i. e. matter cannot be limited by ideas and vice versa.

In philosophical semantics or the philosophy of language, the ' extension ' of a concept or expression is the set of things it extends to, or applies to, if it is the sort of concept or expression that a single object by itself can satisfy.

By extension, the word has also been used to mean any sort of recurring theme, ( whether or not subject to developmental transformation ) in music, literature, or ( metaphorically ) the life of a fictional character or a real person.

Kenneth and Miriam Allott, referring to " Dover Bitch " as " an irreverent jeu d ' esprit ", nonetheless see, particularly in the line " a sort of mournful cosmic last resort ", an extension of the original poem's main theme.

This entrance should be protected by some sort of canopy ( or an extension of the roof ) to reduce or eliminate the formation of dew on the landing platform — large drops of water will tend to trap early leaving bees until the water evaporates.

Sooraya is seen driving a group of Taliban guerillas from a small town and declaring the town to be under her protection, with the Taliban thinking she is some sort of extension of Allah's wrath.

Neil Pigot, who did some work with the group, describes their style as " a sort of extension of the Python tradition, but very much in an Australian context.

The module extension system also used bank-switching and made it theoretically possible to extend to megabytes of RAM ( even more modules could be used by adding expansion devices, yielding sort of a tower ), however neither BASIC nor most of the applications were prepared to use this as free space.

Files with a ". jhtml " filename extension contain standard HTML tags in addition to proprietary tags that reference Java objects running on a special server setup to handle requests for pages of this sort.

One of my virtues or vices is a sort of three-dimensional imagination complete with sound effects and glorious living color.

And if he is so scornful of the rights of states, why not advocate a different sort of constitution that he could more sincerely support??

But the highroad, according to the description of its traffic, belongs to life as it is lived in unawareness of death, while the way to the churchyard belongs to some other sort of life: a suffering form, an existence wholly comprised in the awareness of death.

The hero, who is himself, is represented as a pilgrim in the storied lands of the East, a sort of Faustus type, who, to quote from Professor Book again, `` even in the pleasure gardens of Sardanapalus can not cease from his painful search after the meaning of life.

Merely having a mental image of some sort is not the all-important consideration.

There may be a case of this sort, but it is not one we wish to argue, here.

In his effort to stir the public from its lethargy, Steele goes so far as to list Catholic atrocities of the sort to be expected in the event of a Stuart Restoration, and, with rousing rhetoric, he asserts that the only preservation from these `` Terrours '' is to be found in the laws he has so tediously cited.

An idea, of the sort that we have in mind, although of necessity readily available to imagination, is more general in connotation than most poetic or literary images, especially those appearing in lyric poems that seek to capture a moment of personal experience.

Thus Burns's `` My love is like a red, red rose '' and Hopkins' `` The thunder-purple sea-beach, plumed purple of Thunder '' although clearly intelligible in content, hardly present ideas of the sort with which we are here concerned.

Greek phone service is worse than French, so that it was to be some little time before contact of any sort was established.

It is a matter of trying to sort out an earlier fourth-century Saxon element from the later, fifth-century mainstream of Anglo-Saxon invasions.

It is for these reasons that proposals for a `` new world order '', through radical overhaul of the United Nations or through some sort of world federation, are utterly fatuous.

( It is sort of as if our government should decide to disown Washington or Lincoln for the same reason.

Having hedged its bets in this way, PHS apparently decided it would be possible to make some sort of determination after all: `` At present radiation levels, and even at somewhat higher levels, the additional risk is slight and very few people will be affected ''.

If this practice should take root and spread, the man who submits a manuscript to a publisher will find himself reviewed before he is accepted and publication will become a sort of post-mortem formality.

`` This is the sort of stuff I write and then throw away ''!!

The fruit is then cooled to 42-degrees-F., a temperature at which it lapses into a sort of dormant state.

The reason that we are not going ahead full speed to develop high thrust-to-weight engines is that it would cost perhaps a billion dollars -- and you don't spend that sort of money if aircraft are obsolete.

It is this sort of experience that makes the concept of high fidelity of real musical significance for the home music listener.

As the work progresses the frame and moving parts become a sort of Chinese puzzle where several pieces must be removed before the part you are working on is accessible.

It is a sort of academic ring-around-a-rosy and you solve it.

According to the theory proposed, this is a consequence of the severe condition of perceived threat that persists unabated for the anxious child in an ambiguous sort of school environment.

If, as I suspect, the problem is largely of the second sort, then development of a theory better able to handle tone will result automatically in better theory for all phonologic subsystems.

We need many more studies of this sort if the design of written languages is to be put on a sound basis.

I wished to prepare myself but did not even know what sort of clothes I ought to be wearing.

It did not care what sort of person prowled its woods, plucked at its bark or stripped the berries from its bushes.

The joint investigations of linguistics and psychiatry have established, in point of fact, that no matter what the subject of conversation is or what words are involved, it is impossible for people to talk at all without telling over and over again what sort of people they are and how they relate to the rest of the world.

The work done by the analysts, the men who really know what folklore is all about, has no more appeal than any other work of a truly scientific sort and reaches a limited, learned audience.

It suddenly occurred to me that I did not particularly like acting, that I was at some sort of crossroads and would have to decide soon what I was going to do with my life.

`` You often hear people talk about team spirit and that sort of thing '', Benington said in a conversation after the ceremonies, `` but what this team had was a little different.

He declares at the start: " No matter what sort he is, everyone who has to his credit what are or really seem great achievements, if he cares for truth and goodness, ought to write the story of his own life in his own hand ; but no one should venture on such a splendid undertaking before he is over forty.

Amdahl's law does represent the law of diminishing returns if you are considering what sort of return you get by adding more processors to a machine, if you are running a fixed-size computation that will use all available processors to their capacity.

Thus LTCM failed as a fixed income arbitrage fund, although it is unclear what sort of profit was realized by the banks that bailed LTCM out.

Nahum, taking words from Moses himself, have shown in a general way what sort of " Being God is ".

The Bacardi buildings are exactly the sort that resonate with our consciousness of what Miami is about ".

Searle himself was vague about what extra ingredients it would take to make a machine conscious: all he proposed was that what was needed was " causal powers " of the sort that the brain has and that computers lack.

It is not really fire, for fire is an excess of heat and a sort of ebullition ; but in reality, of what we call air, the part surrounding the earth is moist and warm, because it contains both vapour and a dry exhalation from the earth.

The lecture also gives a sort of insight to what Jesus may have be feeling during the execution from the whippings and beatings, to the crown of thorns, to the nailing on the cross.

His form and expression also tell the person what sort of death they will have: a pained expression means a painful death, a peaceful expression means a peaceful death.

Even before the Declaration of Boulogne, the language was remarkably stable ; only one set of lexical changes were made in the first year after publication, namely changing " when ", " then ", " never ", " sometimes ", " always " from kian, tian, nenian, ian, ĉian to kiam, tiam, neniam etc., to avoid confusion with the accusative forms of kia " what sort of ", tia " that sort of ", etc.

The questions of what defines film noir and what sort of category it is provoke continuing debate.

When animals or people free-run, experiments can be done to see what sort of signals, known as zeitgebers, are effective in entrainment.