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A set is relatively open iff it is equal to its relative interior. Note that when aff ( S ) {\displaystyle \operatorname {aff} (S)} is a closed subspace of the full vector space (always the case when the full vector space is finite dimensional) then being relatively closed is equivalent to being closed.
An optimal clique cover of the line graph () may be formed with one clique for each triangle in that has two or three degree-2 vertices, and one clique for each vertex that has degree at least two and is not a degree-two vertex of one of these triangles. The intersection number is the number of cliques of these two types.
The interior, boundary, and exterior of a set together partition the whole space into three blocks (or fewer when one or more of these is empty): = , where denotes the boundary of . [3] The interior and exterior are always open, while the boundary is closed.
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.
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 ]
Typical values range from 1/5 em to 1/3 em (in digital typography an em is equal to the nominal size of the font, so for a 10-point font the space will probably be between 2 and 3.3 points). Sophisticated fonts may have differently sized spaces for bold, italic, and small-caps faces, and often compositors will manually adjust the width of the ...
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.
In block-style the equation is rendered in its own paragraph and the operators are rendered consuming less horizontal space. The equation is indented. The sum ∑ i = 0 ∞ 2 − i {\displaystyle \sum _{i=0}^{\infty }2^{-i}} converges to 2.