Uniform boundedness principleIn mathematics, the uniform boundedness principle or Banach–Steinhaus theorem is one of the fundamental results in functional analysis. Together with the Hahn–Banach theorem and the open mapping theorem, it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of continuous linear operators (and thus bounded operators) whose domain is a Banach space, pointwise boundedness is equivalent to uniform boundedness in operator norm.
ReykjavíkReykjavík (ˈreɪkjəvɪk,_-viːk ; ˈreiːcaˌviːk) is the capital and largest city of Iceland. It is located in southwestern Iceland, on the southern shore of Faxaflói bay. Its latitude is 64°08' N, making it the world's northernmost capital of a sovereign state. Reykjavík has a population of around 140,000 as of 2023 (up from 121,822 in 2015). The Capital Region has a population of around 248,000. Reykjavík is believed to be the location of the first permanent settlement in Iceland, which, according to Landnámabók, was established by Ingólfr Arnarson in 874 CE.
Baire category theoremThe Baire category theorem (BCT) is an important result in general topology and functional analysis. The theorem has two forms, each of which gives sufficient conditions for a topological space to be a Baire space (a topological space such that the intersection of countably many dense open sets is still dense). It is used in the proof of results in many areas of analysis and geometry, including some of the fundamental theorems of functional analysis.
IntegratorAn integrator in measurement and control applications is an element whose output signal is the time integral of its input signal. It accumulates the input quantity over a defined time to produce a representative output. Integration is an important part of many engineering and scientific applications. Mechanical integrators are the oldest type and are still used for metering water flow or electrical power. Electronic analogue integrators are the basis of analog computers and charge amplifiers.
Vertical integrationIn microeconomics, management and international political economy, vertical integration is an arrangement in which the supply chain of a company is integrated and owned by that company. Usually each member of the supply chain produces a different product or (market-specific) service, and the products combine to satisfy a common need. It contrasts with horizontal integration, wherein a company produces several items that are related to one another.
