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 ′′.

In accordance with the principle on which alphabets are based, these rules will generally map letters of the alphabet to the phonemes ( significant sounds ) of the spoken language.

An abstraction can be seen as a process of mapping multiple different pieces of constituent data to a single piece of abstract data based on similarities in the constituent data, for example many different physical cats map to the abstraction " CAT ".

Some of these simple programs are based on fractal geometry, and can map midi notes to specific fractals, or fractal equations.

The map was based on the 1901 Census of India in which questions about caste and sub-caste were asked of the respondents, the most explicit in the census's history.

Linguistic map representing a Tree model of the Romance languages based on the comparative method.

A map of the Gulag camps, which existed between 1923 and 1961, based on data from the Human Rights Society Memorial ( society ) | " Memorial ".

The world as known to the Hebrews ( based on 1854 map.

Detailed map of Namibia based on the radar map shown below.

It is known that a world map based on the Geographia was on display in Augustodunum, Gaul in late Roman times.

A map of the United States showing the number of electoral votes allocated to each state following Electoral College ( United States )# Apportionment | reapportionment based on the 2010 United States Census | 2010 census ; 270 electoral votes are required for a majority out of 538 overall.

The map of Ming dynasty ( 1433 ), based on The Historical Atlas of China

1690 copy of the 1570 Skálholt map, based on documentary information about earlier Norse sites in America.

There were reports that the number of residents increased by 60 % during the 1990s to about 25, 000 although a second estimate ( based on the 2000 census based on a different map ) places the residential ( nighttime and weekend ) population in 2000 at 12, 042.

* American Regional Accent Map A continuously-updating map based on users ' responses to quizzes

Link State routing protocols build a topographical map of the entire network based on updates from neighbor routers, and then use the Dijkstra algorithm to compute the shortest path to each destination.

It is what a world view ( whether it be based on individual or shared human experience ) ultimately attempts to describe or map.

Lewis and Clark expedition co-leader William Clark produced a map based on the previous expedition and included the explorations of John Colter in 1807, apparently based on discussions between Clark and Colter when the two met in St. Louis, Missouri in 1810.

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 German cosmographer and mathematician, Johannes Schöner ( 1477 – 1547 ) constructed a terrestrial globe in 1515, based on the world map and globe made by Martin Waldseemüller and his colleagues at St. Dié in Lorraine in 1507.

The cartographic depictions of the southern continent in the 16th and early 17th centuries, as might be expected for a concept based on such abundant conjecture and minimal data, varied wildly from map to map ; in general, the continent shrank as potential locations were reinterpreted.

The map location is based on sensed antenna direction and