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 ′′.

Although the Cantino planisphere ( 1504 ) and the Ruysch map ( 1507 ) clearly delineate the Maldive Islands, giving them the same names, they do not show any islands to the south which can be identified as the Chagos archipelago.

A map of Luxembourg's relief clearly illustrates the dichotomy between the hilly Oesling in the north and the southern Gutland ( Luxembourg ) | Gutland.

For example, a road map may not show railroads, smaller waterways or other prominent non-road objects, and even if it does, it may show them less clearly ( e. g. dashed or dotted lines / outlines ) than the main roads.

The designers of the map have tackled a variety of problems in showing information as clearly as possible and have sometimes adopted different solutions.

Streeter clearly lied about his discovery of the " District of Lake Michigan " in 1886, referencing a map published in 1821 to determine that his " District " was outside of City limits.

The layout of the town as depicted in Speed's map of 1610 would be easily recognisable to present day inhabitants, with the layout of the main axis clearly visible from the castle via the main street, Monnow Street, to the bridge.

As is shown clearly on the map, the jus soli is mainly in use in “ the new world ” — the Americas.

The map clearly shows the Bay of Nuku ' alofa and his anchored position near Pangaimotu.

The same changes marked more clearly on another map

" He ensured that all his men received a map of Nanking and vicinity, with the Zhongshan Tomb ( where Sun Yatsen is interred ), the Ming Xiao Tomb, foreign legations, and other places where they were prohibited from entering clearly marked, and ordered sentries to be posted at each one of them.

An excellent map, known as the Al Idrisi map from the calligrapher who developed it and dated from the 1160s, clearly depicts an accurate representation of Lake Victoria, and attributes it as the source of the Nile.

A map from the 1840s-1850s in the Quaker Collection of Earlham College in Richmond, Indiana, clearly shows a county named Richardville, and a town Richardville, at the site of present-day Russiaville.

In Philip Pullman's less well-known little book " Lyra's Oxford " there is a pull-out map which clearly shows the building we know as Exeter College to be Jordan College.

As Ermine Street extended north out of Lincoln and past RAF Scampton the map attached clearly shows an alternative course of Ermine Street curving left and forming a semicircle on a wide heading west of the Humber Estuary.

According to Szabolcsi, these ' Hungarian transpositions ', along with " some melodic, rhythmical and ornamental peculiarities, clearly show on the map of Eurasia the movements of Turkish people from the East to the West ".

** NB a map in the * Romney Marsh Gazetteer shows the stages clearly.

John Rocque shows the road very clearly on his large scale map of 1746, however the names have changed again.

Wendy Suart wrote in her book on North Borneo, The Lingering Eye, " there is in the Sabah State Museum a Dutch map of Borneo and the Celebes dated 1657 in which the settlement where Jesselton was to stand is clearly labelled Api Api.

The map clearly showed the Roman Cardo as the main artery through the Old City.

The first map of Southwark ( Duchy of Lancaster ca1543 ) clearly shows it marked as ' Gorge '.

But it was clearly Beck who had the idea of creating a full system map in colour.

North-to-south cuts gouged by the ice can be seen clearly on the map: they form the West Passage that separates Conanicut Island from the western mainland and the East Passage that now separates Conanicut Island from Aquidneck Island.