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.
IcelandIceland (Ísland, ˈistlant) is a Nordic island country between the North Atlantic and Arctic Oceans, on the Mid-Atlantic Ridge between North America and Europe. It is linked culturally and politically with Europe, and is the region's most sparsely populated country. Its capital and largest city is Reykjavík, which is home to about 36% of the country's roughly 380,000 residents. Located on a rift between tectonic plates, Iceland's geologic activity includes geysers and frequent volcanic eruptions.
Closed graph theoremIn mathematics, the closed graph theorem may refer to one of several basic results characterizing continuous functions in terms of their graphs. Each gives conditions when functions with closed graphs are necessarily continuous. Closed graph If is a map between topological spaces then the graph of is the set or equivalently, It is said that the graph of is closed if is a closed subset of (with the product topology). Any continuous function into a Hausdorff space has a closed graph.
SequenceIn mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. Like a set, it contains members (also called elements, or terms). The number of elements (possibly infinite) is called the length of the sequence. Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. Formally, a sequence can be defined as a function from natural numbers (the positions of elements in the sequence) to the elements at each position.
Closed graph propertyIn mathematics, particularly in functional analysis and topology, closed graph is a property of functions. A function f : X → Y between topological spaces has a closed graph if its graph is a closed subset of the product space X × Y. A related property is open graph. This property is studied because there are many theorems, known as closed graph theorems, giving conditions under which a function with a closed graph is necessarily continuous. One particularly well-known class of closed graph theorems are the closed graph theorems in functional analysis.
