It is usually helpful to make a sketch map in the field, showing the size and location of the features of interest and to take photographs at the site.

Korzybski is remembered as the author of the dictum: " The map is not the territory ".

This was expressed by Korzybski's most famous premise, " the map is not the territory ".

* The map is not the territory

** Tarski's theorem: For every infinite set A, there is a bijective map between the sets A and A × A.

** On every infinite-dimensional topological vector space there is a discontinuous linear map.

** In the category of Riemann surfaces, an automorphism is a bijective biholomorphic map ( also called a conformal map ), from a surface to itself.

Later, his published letters were the basis of Waldseemüller's 1507 map, which is the first usage of America.

" " Giving Directions " is the term for thinking and projecting an anatomically ideal map of how one's body may be used effortlessly.

The first major application was the relative version of Serre's theorem showing that the cohomology of a coherent sheaf on a complete variety is finite dimensional ; Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent ; this reduces to Serre's theorem over a one-point space.

The map is oriented with south at the top.

A map of Cyprus in the later Bronze Age ( such as is given by J. L. Myres and M. O. Richter in Catalogue of the Cyprus Museum ) shows more than 25 settlements in and about the Mesaorea district alone, of which one, that at Enkomi, near the site of Salamis, has yielded the richest Aegean treasure in precious metal found outside Mycenae.

Celsius conducted many geographical measurements for the Swedish General map, and was one of earliest to note that much of Scandinavia is slowly rising above sea level, a continuous process which has been occurring since the melting of the ice from the latest ice age.

The associator is a trilinear map given by

By definition a multilinear map is alternating if it vanishes whenever two of its arguments are equal.

More precisely, a binary operation on a non-empty set S is a map which sends elements of the Cartesian product S × S to S:

Furthermore, a map f: A → B is a homomorphism of Boolean algebras if and only if it is a homomorphism of Boolean rings.

There is a natural map F: X → X ′′ ( the dual of the dual

Because F ( x ) is a map from X ′ to K, it is an element of X ′′.

The map F: x → F ( x ) is thus a map X → X ′′.

rightMariner 8 and Mariner 9 were identical sister craft designed to map the Martian surface simultaneously, but Mariner 8 was lost in a launch vehicle failure.

The wall map was lost for a long time, but a copy was found in Schloss Wolfegg in southern Germany by Joseph Fischer in 1901.

If a player dies all their weapons are lost and they receive the spawn weapons for the current map, usually the gauntlet and machine gun.

This text sheds light on aspects of Jan van Eyck's production now lost, citing a bathing scene owned by a prominent Italian, but mistakenly attributing to van Eyck a world map painted by another.

The first depiction of Terra Australis on a globe was probably on Johannes Schöner's lost 1523 globe on which Oronce Fine is thought to have based his 1531 double cordiform ( heart-shaped ) map of the world.

The web site also offers new " profiles " of teams and players full of facts and statistics that hope to one day map what James has termed " the lost island of baseball statistics.

( Users can enable a map of the desktops, in case they get lost, which is called the pager.

" While rummaging through the Walshes ' attic, they find an old newspaper clipping, a Spanish map, and an artifact relating to a rumor of a lost but not forgotten pirate treasure somewhere in the area.

While a map or GPS would make it easy, drivers or cyclists without those tools would likely get lost.

According to folklore, a lost map from 809 made reference to a fiefdom " Bodelo ".

A treasure map is a variation of a map to mark the location of buried treasure, a lost mine, a valuable secret or a hidden location.

In a eulogy for Smith printed in the Illinois Magazine for June 1832 the unknown author claimed “ This map is now probably the best extant, of the Rocky Mountains, and the country on both sides, from the States to the Pacific .” The original map is lost, its content was superimposed probably by George Gibbs on a base map by John C. Frémont, which is on file at the American Geographical Society Library, at the University of Wisconsin-Milwaukee.

In the development of the Dreamcast version of the original arcade game, the developers included a larger map in addition to the arcade one, as to create a feeling of " being lost " and allowing home console players to have fun " learning the town ".

Though the Empire lost several western territories after the secession of the Seven United Netherlands in 1581 and during the French annexations of the 1679 Peace of Nijmegen, the ten circles remained largely unchanged until the early 1790s, when the French Revolutionary Wars brought about significant changes to the political map of Europe.

Each of the boards has a map, so it is difficult to get lost.

Heading north much of the route is lost, since Codrington wrote, in the development of Redditch, however Icknield Street Drive, Battens Drive approximates the route until a small road through the residential area of Churchill marked Ryknield Street on the modern 1: 25, 000 Ordnance Survey map, exactly in a line with Haydon Way, is reached.

Most of the complete copies of the atlas have been lost or destroyed ( often by fire ), although a mostly-complete copy of the large-scale map was discovered in the collection of the U. S. Library of Congress in 2001.

On a map he made of the wreck site Southack reported that he had buried 102 of the 144 Whydah crew and captives lost in the sinking ( though technically they were buried by the town coroner, who surprised Southack by handing him the bill and demanding payment ).

The z z < sup > n </ sup > mapping shows this as a local pattern: if we exclude 0, looking at 0 < | z | < 1 say, we have ( from the homotopy point of view ) the circle mapped to itself by the n-th power map ( Euler-Poincaré characteristic 0 ), but with the whole disk the Euler-Poincaré characteristic is 1, n – 1 being the ' lost ' points as the n sheets come together at z = 0.

Author Robert M. Pirsig uses the idea both theoretically and literally in his book Lila when the main character / author becomes temporarily lost due to an over reliance on a map, rather than the territory that the map describes.

* Orchestrate the elements of the map to best convey its message to its audience.

Yet those are all a typical passenger wishes to know, so the map fulfils its purpose.

" Robinson codified the mapmaker's understanding that a map must be designed foremost with consideration to the audience and its needs.

The intent of the map should be illustrated in a manner in which the percipient acknowledges its purpose in a timely fashion.

In order to convey the message of the map, the creator must design it in a manner which will aid the reader in the overall understanding of its purpose.

The quality of a map's design affects its reader's ability to extract information and to learn from the map.

A legend explains the pictorial language of the map, known as its symbology.

* It is essential for U to be simply connected for the function f to be globally invertible ( under the sole condition that its derivative is a bijective map at each point ).

The first map to delineate the island under its present name, Diego Garcia, is the World Map of Edward Wright ( London 1599 ), possibly as a result of misreading Dio ( or simply " D .") as Diego, and Gratia as Garcia.

The Taylor series of the map is F ( x ) = J · x + O ( x < sup > 2 </ sup >), so a change of coordinates h can only be expected to simplify F to its linear part

Indeed, the map of Barsaive and its neighboring regions established that most of the game takes place where the Ukraine and adjacent Russia are in our world.

Appearing with the term, and helping spread and sustain its popularity, was a political cartoon depicting a strange animal with claws, wings and a dragon-type head satirizing the map of the odd shaped district.

Power sets: The power set functor P: Set → Set maps each set to its power set and each function to the map which sends to its image.

Dual vector space: The map which assigns to every vector space its dual space and to every linear map its dual or transpose is a contravariant functor from the category of all vector spaces over a fixed field to itself.

Tangent and cotangent bundles: The map which sends every differentiable manifold to its tangent bundle and every smooth map to its derivative is a covariant functor from the category of differentiable manifolds to the category of vector bundles.

Likewise, the map which sends every differentiable manifold to its cotangent bundle and every smooth map to its pullback is a contravariant functor.