Borough of Berwick-upon-Tweed Borough of Berwick-upon-Tweed Berwick-upon-Tweed was a local government district and borough in Northumberland in the north-east of England, on the border with Scotland. The district had a resident population of 25,949 according to the 2001 census, which also notes that it is the most ethnically homogeneous in the country, with 99.6% of the population recording themselves in the 2001 census as "White". It was also the smallest district in England with borough status, and the third-least densely populated local government district (after Eden and Tynedale). Its main town is Berwick-upon-Tweed, sited immediately to the north of the Tweed estuary. The
Densely defined operator Densely defined operator In mathematics – specifically, in operator theory – a densely defined operator or partially defined operator is a type of partially defined function. In a topological sense, it is a linear operator that is defined "almost everywhere". Densely defined operators often arise in functional analysis as operations that one would like to apply to a larger class of objects than those for which they "a priori" "make sense". A densely defined linear operator "T" from one topological vector space, "X", to another one, "Y", is a linear operator that is defined on a dense linear subspace dom("T")