Pointwise convergenceIn mathematics, pointwise convergence is one of various senses in which a sequence of functions can converge to a particular function. It is weaker than uniform convergence, to which it is often compared. Suppose that is a set and is a topological space, such as the real or complex numbers or a metric space, for example. A net or sequence of functions all having the same domain and codomain is said to converge pointwise to a given function often written as if (and only if) The function is said to be the pointwise limit function of the Sometimes, authors use the term bounded pointwise convergence when there is a constant such that .
V2 word orderIn syntax, verb-second (V2) word order is a sentence structure in which the finite verb of a sentence or a clause is placed in the clause's second position, so that the verb is preceded by a single word or group of words (a single constituent). Examples of V2 in English include (brackets indicating a single constituent): "Neither do I", "[Never in my life] have I seen such things" If English used V2 in all situations, then it would feature such sentences like: "[In school] learned I about animals", "[When she comes home from work] takes she a nap" V2 word order is common in the Germanic languages and is also found in Northeast Caucasian Ingush, Uto-Aztecan O'odham, and fragmentarily in Romance Sursilvan (a Rhaeto-Romansh variety) and Finno-Ugric Estonian.
Radius of convergenceIn mathematics, the radius of convergence of a power series is the radius of the largest disk at the center of the series in which the series converges. It is either a non-negative real number or . When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges.
Compact convergenceIn mathematics compact convergence (or uniform convergence on compact sets) is a type of convergence that generalizes the idea of uniform convergence. It is associated with the compact-open topology. Let be a topological space and be a metric space. A sequence of functions is said to converge compactly as to some function if, for every compact set , uniformly on as . This means that for all compact , If and with their usual topologies, with , then converges compactly to the constant function with value 0, but not uniformly.
