Although it seems to have skyrocketed from science fiction novels, this is something that has been seriously considered to cut down on heating costs.
It is the project that the famous modernist architect named Buckminster Fuller thinks seriously and plans to build through geodesic domes. He claimed that it would be profitable no matter how high the initial cost would be, as the air conditioning with this method would reduce the heating costs to almost zero, and in 1960 proposed to cover Manhattan with a completely transparent dome.
Although it looks like a science fiction, it is not impossible to build such huge domes as geodesic domes become more efficient as they grow and can be built quite easily. As a matter of fact, even though the fuller is not in the size of a city, it tried this idea in its structure called Montreal Biosphere and successfully built the dome. Unfortunately, when a big fire broke out in the dome and the building was seriously damaged, it was noticed that a dome on Manhattan would be vulnerable to fires, and the city project in the lantern was completely shelved.
With the invention of fireproof plastic polymers half a century after Fuller, the architects have solved the fire, and they decided to take the city into a lantern this time. Although not exactly as we imagined, Grimshaw Architects managed to take huge areas inside the lantern with the Eden Project, using geodesic domes, as Fuller predicted.
However, interestingly, although the project was successful, it has been largely ignored by the architectural and urban planning environments.
Technically, it is possible to encircle cities and even make sense. But the idea is so unusual and varied that no one dares to do it for now.