A ruling is expected by mid-January.
The Supreme Court president, Lord Neuberger, closed the hearing by highlighting that the court was not there to "overturn the result of the EU referendum" which favoured an exit from the economic bloc in June 23.
"We are not being asked to overturn the result of the EU referendum, we are being asked to determine the process by which that result can be brought into effect. That raises important constitutional issues and we will now make sure that the many arguments are given full and proper consideration. We appreciate that this case should be resolved as quickly as possible and we will do our best to achieve that," he said.
May has promised to give notice of the UK's departure from the EU under Article 50 of the Lisbon Treaty by the end of March 2017 - a timetable that was backed by MPs in the Commons vote last night.
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However, Downing Street has said that it would not override the Supreme Court if it rules that legislation is required before notice of Brexit is served.
The government had lost last month's High Court case, leading to the landmark appeal in the Supreme Court heard by all 11 justices of Britain's highest court.
"I know that around the world people have been amazed at the incredible efficiency shown by the judges, lawyers and all of the parties involved in this case who have shoe-horned around two years of work into six months to ensure the PM can trigger Article 50 before the end of March.
"I hope the Supreme Court will uphold the High Court ruling that Article 50 cannot be triggered using the royal prerogative. Our case is that prerogative powers end where domestic law begins," said Gina Miller, an investment fund manager named as the lead claimant in the legal fight to get Parliament to vote on whether the UK government can start the process of leaving the EU.
He also pointed out that the House of Commons vote last night in favour of invoking Article 50 by March 31, 2017, was "highly significant" and provides "the sharpest of focus" for the court.
"It may not be legally binding but that does not mean it is not legally relevant, because Parliament has given specific approval to the Government to give that notice. Parliament has indicated its view and has done so clearly," he said.
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