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Holomorphic function: complex-valued function of a complex variable which is differentiable at every point in its domain. Meromorphic function: complex-valued function that is holomorphic everywhere, apart from at isolated points where there are poles. Entire function: A holomorphic function whose domain is the entire complex plane.
Sometimes, if each function in a normal family F satisfies a particular property (e.g. is holomorphic), then the property also holds for each limit point of the set F. More formally, let X and Y be topological spaces. The set of continuous functions : has a natural topology called the compact-open topology. A normal family is a pre-compact ...
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
The Dirac comb of period 2 π, although not strictly a function, is a limiting form of many directional distributions. It is essentially a wrapped Dirac delta function. It represents a discrete probability distribution concentrated at 2 π n — a degenerate distribution — but the notation treats it as if it were a continuous distribution.
The term "family values" is often used in political discourse in some countries, its general meaning being that of traditional or cultural values that pertain to the family's structure, function, roles, beliefs, attitudes, and ideals, usually involving the "traditional family"—a middle-class family with a breadwinner father and a homemaker ...
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This is a list of gene families or gene complexes, i.e. sets of genes which are related ancestrally and often serve similar biological functions.These gene families typically encode functionally related proteins, and sometimes the term gene families is a shorthand for the sets of proteins that the genes encode.
Additionally, a family of sets may be defined as a function from a set , known as the index set, to , in which case the sets of the family are indexed by members of . [1] In some contexts, a family of sets may be allowed to contain repeated copies of any given member, [ 2 ] [ 3 ] [ 4 ] and in other contexts it may form a proper class .