The landscaping of the park space and later the Winter Garden was designed by M. Paul Friedberg.

In mathematics, a contraction mapping, or contraction, on a metric space ( M, d ) is a function f from M to itself, with the property that there is some nonnegative real number < math > k < 1 </ math > such that for all x and y in M,

Moreover, the Banach fixed point theorem states that every contraction mapping on a nonempty complete metric space has a unique fixed point, and that for any x in M the iterated function sequence x, f ( x ), f ( f ( x )), f ( f ( f ( x ))), ... converges to the fixed point.

Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.

Then the cotangent space at x is defined as the dual space of T < sub > x </ sub > M:

Concretely, elements of the cotangent space are linear functionals on T < sub > x </ sub > M.

Then I < sub > x </ sub > and I < sub > x </ sub >< sup > 2 </ sup > are real vector spaces and the cotangent space is defined as the quotient space T < sub > x </ sub >< sup >*</ sup > M = I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup >.

Since the map d restricts to 0 on I < sub > x </ sub >< sup > 2 </ sup > ( the reader should verify this ), d descends to a map from I < sub > x </ sub > / I < sub > x </ sub >< sup > 2 </ sup > to the dual of the tangent space, ( T < sub > x </ sub > M )< sup >*</ sup >.

The k-th exterior power of the cotangent space, denoted Λ < sup > k </ sup >( T < sub > x </ sub >< sup >*</ sup > M ), is another important object in differential geometry.

The algebra M < sub > n </ sub >( C ) of n-by-n matrices over C becomes a C *- algebra if we consider matrices as operators on the Euclidean space, C < sup > n </ sup >, and use the operator norm ||.|| on matrices.

In mathematical analysis, a metric space M is called complete ( or a Cauchy space ) if every Cauchy sequence of points in M has a limit that is also in M or, alternatively, if every Cauchy sequence in M converges in M.

Experience is not seen, as it is in classical rationalism, as presenting us initially with clear and distinct objects simply located in space and registering their character, movements, and changes on the tabula rasa of an uninvolved intellect.

It is notable that at this time he was writing with admiration of Cimabue's and Poussin's way of filling space.

Next I refer to our program in space exploration, which is often mistakenly supposed to be an integral part of defense research and development.

Third, the United States is pressing forward in the development of large rocket engines to place vehicles of many tons into space for exploration purposes.

Like ours, the economy of the space merchants must constantly expand in order to survive, and, like ours, it is based on the principle of `` ever increasing everybody's work and profits in the circle of consumption ''.

And this, of course, is exactly what Madison Avenue has been accused of doing albeit in a primitive way, with its `` hidden persuaders '' and what the space merchants accomplish with much greater sophistication and precision.

Thus the copywriter in the world of the space merchants is the person who in earlier ages might have been a lyric poet, the person `` capable of putting together words that stir and move and sing ''.

But there is hope, for Conservation Commissioner Bontempo has tagged the sanctuary as the kind of place the state hopes to include in its program to double its park space.

Four hundred million dollars of the increase is for the expanded space program, a responsibility similarly neglected by Mr. Eisenhower.

I would like to see you devote some space in an early issue to the news blackout concerning President Kennedy's activities, so far as Southern California is concerned.

Advice is given also on problems of plant location and plant space.

The outside 4-inch space is filled by mortaring blocks on edge.

The space between them is filled with pit-run gravel or earth.

In general, such apartments afford more protection than smaller buildings because their walls are thick and there is more space.

The problem for the city apartment dweller is primarily to plan the use of existing space.

The music is always allowed the living space needed to attain its full sonority ; ;

But if space and money are no problem and small children are not on hand every day, it is certainly more restful to have your pool and entertainment area removed from the immediate environs of the house.

Since there is a continual loss of micrometeoritic material in space because of the radiation effects, there must be a continual replenishment: otherwise, micrometeorites would have disappeared from interplanetary space.

With detectors sensitive to three mass intervals and based on a few counts, the second and third Russian space probes indicate that the flux of the smallest particles detected is less than that of larger ones.

Of course, if there is a dust blanket around the Earth, the fluxes in interplanetary space should be less than the figures given here.

If ( remember this is an assumption ) the minimal polynomial for T decomposes Af where Af are distinct elements of F, then we shall show that the space V is the direct sum of the null spaces of Af.

Conversely, suppose that **ya is in the null space of Af.

This puts a fine point on the idea of taking " steps " in a space.

Forming the damp paste into corn-sized clumps by hand or with the use of a sieve instead of larger balls produced a product after drying that loaded much better, as each tiny piece provided its own surrounding air space that allowed much more rapid combustion than a fine powder.

extremely fine lines ( less than 50 nm line and space has been achieved ) without proximity

However, the product topology is " correct " in that it makes the product space a categorical product of its factors, whereas the box topology is too fine ; this is the sense in which the product topology is " natural ".

More precisely, space can be viewed as an extremely fine fabric or network " woven " of finite loops.

The most notable archetypes are Street Samurai, characters who have heavily augmented their bodies with cyberware and bioware and focus on physical combat ; Adepts, characters who have magical abilities that increase their physical ( and sometimes mental ) combat abilities ; Faces, highly charismatic characters who specialize in negotiations and social manipulation ; Hackers ( aka Deckers ), specialize in electronic surveillance, security, and augmented / virtual reality monitoring, combat and response ; Riggers, who augment their brains to achieve fine control over vehicles and drones ; and Magicians who cast spells and can view emotions and call spirits from astral space.

Matrix is very fine material, which is present within interstitial pore space between the framework grains.

At its opening, some critics thought that Taniguchi's design was a fine example of contemporary architecture, while many others were extremely displeased with certain aspects of the design, such as the flow of the space.

In the 1950s local artists offered space in their homes for fine arts and crafts.

Known for its fine old homes, its heavily wooded lots and its beautiful watercourses, the controlling of commercial development and the preservation of open space have been the chief political issues in Holladay's recent history.

More precisely, space can be viewed as an extremely fine fabric or network " woven " of finite loops.

A new format feature, the divided page, was designed to save space by including a section of words below the line at the bottom of each page: six columns of very fine print, devoted to such items as rarely used, obsolete, and foreign words, abbreviations, and variant spellings.

His work encompasses portraits, landscapes, aviation and space, ships, cars and his new collection of cat-related fine art paintings.

The scope of inventory management concerns the fine lines between replenishment lead time, carrying costs of inventory, asset management, inventory forecasting, inventory valuation, inventory visibility, future inventory price forecasting, physical inventory, available physical space for inventory, quality management, replenishment, returns and defective goods, and demand forecasting.

The scope of inventory management also concerns the fine lines between replenishment lead time, carrying costs of inventory, asset management, inventory forecasting, inventory valuation, inventory visibility, future inventory price forecasting, physical inventory, available physical space for inventory, quality management, replenishment, returns and defective goods and demand forecasting.

A typical design is a stack of fine metal wire meshes, with low porosity to reduce dead space, and with the wire axes perpendicular to the gas flow to reduce conduction in that direction and to maximize convective heat transfer.

* On a fine scale, it includes logical development of topics, emphasis on what's important, clear writing, navigational clues, and even page design, choice of font, and use of white space.

In front of the palace lies an open space with a fine view over the valley of the Loire.

The Wexner Center, hotly anticipated as the first major public deconstructivist building, has required extensive and expensive retrofitting because of elementary design flaws ( such as incompetent material specifications, and fine art exhibition space exposed to direct sunlight ).

Heuristically, if we have a space M for which each point m ∈ M corresponds to an algebro-geometric object U < sub > m </ sub >, then we can assemble these objects into a topological family U over M. ( For example, the Grassmanian G ( k, V ) carries a rank k bundle whose fiber at any point ∈ G ( k, V ) is simply the linear subspace L ⊂ V .) We say that such a family is universal if any family of algebro-geometric objects T over any base space B is the pullback of U along a unique map B → M. A fine moduli space is a space M which is the base of a universal family.