Is "Glasgow area" a compound noun? Can we write "Glasgow Area"?
Glasgow area is in lower case in the Oxford Dictionary in the definition of confine:
The work will not be confined to the Glasgow area.
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"Glasgow" is the proper noun, the name of the place, so only "Glasgow" is capitalized: "Glasgow area" to refer to the area of and around Glasgow.
OTOH, "New York City" is the name, the proper noun, (to distinguish from the state of the same name), so all three words start with a capital.