Demography of Cumbria is bordered with Scotland to the north, the Irish Sea to the west, Northumberland to the north-east, County Durham to the east and North Yorkshire to the south-east. Carlisle is the largest and only city in the county, whilst Barrow-in-Furness (the largest town) is twice as large as the second largest town (Kendal). The twenty most populous settlements in Cumbria are listed below. Cumbria as a whole is the second least densely populated county in England with only 73 people per square kilometre. Despite it being the third largest in area (6,768 km²), about a third of the county is
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