Libraries in Canada have the same stipulations, but are actually funded and are open all the time. Our downtown library is open 9am-9pm every day of the year.
I live in Canada in a mid-sized city and my library is closed on Sundays. Just as a poster above, it appears to be the case that the librarians negotiated a great deal for themselves. (Closed on Sundays during the summer, open on Sundays during the winter.)
However, it is a great library. No arguments there. It's a pain that its closed on Sundays just when kids want to use it most.
Which city? I'm in a mid-sized city as well. I find it quite surprising since I've lived in many places around Canada from small towns to big cities from Toronto all the way out to the West Coast, and have never had access to at least one library that was open all the time.