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 of "X" and takes values in "Y", written "T" : dom("T") ⊆ "X" → "Y". Sometimes this is abbreviated as "T" : "X" → "Y" when the context makes it clear that "X" might not be the set-theoretic domain of "T". 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