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 ′′.

Villeroi still believed ( on 22 May ) the Allies were a full day ’ s march away when in fact they had camped near Corswaren waiting for the Danish squadrons to catch up ; for his part, Marlborough deemed Villeroi still at Jodoigne when in reality he was now approaching the plateau of Mont St. André with the intention of pitching camp near Ramillies ( see map at right ).

An example of a now discredited " ethnographic " map of India from the Imperial Gazetteer of India, 1909, purporting to show the different " races " ( in coloured regions ), and castes ( in labels ).

Aerial map of the Compaq headquarters, now the Hewlett-Packard USA campus in unincorporated area | unincorporated Harris County, Texas

The flow now defines a map, the Poincaré map F: S → S, for points starting in S and returning to S. Not all these points will take the same amount of time to come back, but the times will be close to the time it takes x < sub > 0 </ sub >.

A map showing the outline of those parts now adjacent to the traditional county of Essex ( in grey ) but which historians postulate were part of the ancient Kingdom of Essex before becoming detached during the middle of the 8th Century.

The evidence is found in two early maps, one made by the Portuguese cartographer Pedro Reinel in about 1522, the very first map to show the Falklands, the other a French copy of a Portuguese map bought in Lisbon by André Thévet ( 1516-1590 ), a Franciscan friar and prolific writer on many subjects ; this copy is now in the manuscript of a large unpublished work by Thevet in the Bibliothèque nationale de France in Paris.

Oyster cards ( the ticket-free system for London Underground ) are now given with wallets sponsored by IKEA who also sponsor the tube map.

The first historical evidence of the existence of an island now known as Mauritius is on a map produced by the Italian cartographer Alberto Cantino in 1502.

The song is a lively mazurka with lyrics penned by Józef Wybicki in Reggio nell ' Emilia, Cisalpine Republic ( now in Italy ), around 16 July 1797, two years after the Third Partition of Poland erased the once vast country from the map.

A number of years ago, a Sorbonne professor discovered an ancient map depicting the site of the cemetery, which now lay under an open square in the city of Troyes.

Stations that can be walked between are now shown, often with the distance between them ( this is an evolution of the pedestrian route between Bank and Monument stations, which was once prominently marked on the map ).

It lists a number of peoples, such as the Hwicce, who have now vanished, except for reminders in various placenames ( see map at the head of this article ).

Broca's area is now typically defined in terms of the pars opercularis and pars triangularis of the inferior frontal gyrus, represented in Brodmann's cytoarchitectonic map as areas 44 and 45 of the dominant hemisphere.

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.

A controversy in the 1980s over the Peters map motivated the American Cartographic Association ( now Cartography and Geographic Information Society ) to produce a series of booklets ( including Which Map is Best ) designed to educate the public about map projections and distortion in maps.

One early map shows a village called Ossachite at the site of what is now downtown Jacksonville ; this may be the earliest recorded name for that area.

As late as 1716, Guillaume Delisle's map of Paris shows that a short stretch of roads and fields and market garden plots still separated the grand axe of the Tuileries gardens from the planted " Avenue des Thuilleries ," stretches west from a newly cleared Place du Pont Tournant soon to be renamed for Louis XV and now the Place de la Concorde.

Harrisse believed the large estuary just west of the line on the Cantino map was that of the Rio Maranhão ( this estuary is now the Baía de São Marcos and the river is now the Mearim ), whose flow is so weak that its gulf does not contain fresh water.

Although every map element serves some purpose, convention only dictates inclusion of some elements, while others are considered optional.

Both map versions of the title BS Zelda no Densetsu for the Satellaview ( released in August and December 1995 ) could be considered spin-offs due to the fact that they star the " Hero of Light " ( portrayed by either the Satellaview's male or female mascot ) as opposed to Link as the protagonist of Hyrule.

Risk could be considered a wargame ; it uses an area map of the Earth and is unabashedly about sending out armies to conquer the world.

In the video game industry, " wargames " are considered a subgenre of strategy game that emphasizes strategic or tactical warfare on a map.

The symbol used on the map for each of these levels at a particular observation time will be for the genus, species, variety, mutation, or cloud motion that is considered most important according to criteria set out by the World Meteorological Organization ( WMO ).

Thus, a random function can be considered to map each input independently at random to any one of the possible outputs.

Two more partition plans were also considered: Plan B ( map ) and Plan C ( map ).

For example, in the category Div of divisible ( abelian ) groups and group homomorphisms between them there are monomorphisms that are not injective: consider, for example, the quotient map q: Q → Q / Z, where Q is the rationals under addition, Z the integers ( also considered a group under addition ), and Q / Z is the corresponding quotient group.

It is often considered to include the graphic representation of the landform on a map by a variety of techniques, including contour lines, hypsometric tints, and relief shading.

Taylor County is considered part of West Texas, but on the state map, it appears in a more central, than western, location.

For a 1920s map of what at that time was considered to be Kensal Green, see Brent Council local history.

Seen on a map, the Ruhr could be considered a single city, since — at least in the north-south dimension — there are no visible breaks between the individual city boroughs.

No link is considered to have been correctly reported unless the two ends agree ; i. e. if one node reports that it is connected to another, but the other node does not report that it is connected to the first, there is a problem, and the link is not included on the map.

Given two tensor bundles E → M and F → M, a map A: Γ ( E ) → Γ ( F ) from the space of sections of E to sections of F can be considered itself as a tensor section of if and only if it satisfies A ( fs ,...) = fA ( s ,...) in each argument, where f is a smooth function on M. Thus a tensor is not only a linear map on the vector space of sections, but a C < sup >∞</ sup >( M )- linear map on the module of sections.

There are two maps depicting North America, the " Vinland map ", that some believe is related to Norse exploration, although it is considered to be a modern forgery, and the Skálholt Map, made by an Icelandic teacher in 1570.

If we take E to be the sum of the even exterior powers of the cotangent bundle, and F to be the sum of the odd powers, define D = d + d *, considered as a map from E to F. Then the topological index of D is the Euler characteristic of the Hodge cohomology of M, and the analytical index is the Euler class of the manifold.

This map is lost and its contents are unknown However, later Roman geographers, including Ptolemy ( AD 90 – c. AD 168 ) ( II. 10, III. 7 ) and Tacitus ( AD 56 – AD 117 ) ( ref: Germania XLVI ) considered the Vistula as the boundary between Germania and Sarmatia Europaea, or Germania and Scythia ..

So it is considered important to be aware that people's beliefs about reality and their awareness of things ( the " map ") are not reality itself or everything they could be aware of (" the territory ").

Notice that if is considered as a map to i. e.: then the double point can be resolved to an embedding:.

A geographical map showing territories commonly considered part of the Near East.