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A city block, residential block, urban block, or simply block is a central element of urban planning and urban design. In a city with a grid system, the block is the smallest group of buildings that is surrounded by streets. City blocks are the space for buildings within the street pattern of a city, and form the basic unit of a city's urban ...
In computational geometry, the largest empty rectangle problem, [2] maximal empty rectangle problem [3] or maximum empty rectangle problem, [4] is the problem of finding a rectangle of maximal size to be placed among obstacles in the plane. There are a number of variants of the problem, depending on the particularities of this generic ...
As a result, the empty set is the unique initial object of the category of sets and functions. The empty set can be turned into a topological space, called the empty space, in just one way: by defining the empty set to be open. This empty topological space is the unique initial object in the category of topological spaces with continuous maps.
A partition of a set X is a set of non-empty subsets of X such that every element x in X is in exactly one of these subsets [2] (i.e., the subsets are nonempty mutually disjoint sets). Equivalently, a family of sets P is a partition of X if and only if all of the following conditions hold: [ 3 ]
Consequently, if these set are not empty [note 1] then they form a partition of . A point is a boundary point of a set if and only if every neighborhood of contains at least one point in the set and at least one point not in the set. The boundary of the interior of a set as well as the boundary of the closure of a set are both contained in the ...
When is empty, the condition given above is an example of a vacuous truth. So the intersection of the empty family should be the universal set (the identity element for the operation of intersection), [4] but in standard set theory, the universal set does not exist.
Similarly, two sheets of A4 can be scaled down to fit one A4 sheet without excess empty paper. This system also simplifies calculating the weight of paper. Under ISO 536 , paper's grammage is defined as a sheet's mass in grams (g) per area in square metres (unit symbol g/m 2 ; the nonstandard abbreviation "gsm" is also used). [ 5 ]
In this case, a Euclidean vector is an element of a normed vector space of finite dimension over the reals, or, typically, an element of the real coordinate space equipped with the dot product. This makes sense, as the addition in such a vector space acts freely and transitively on the vector space itself.