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Andy and Jamie Murray were going to play in the doubles.
The Battle of the Brits, an exhibition featuring Jamie Murray and Andy Murray, has been put off because of rising coronaviruses.
The men's team event between Scotland and England was going to be held in Aberdeen.
The Murrays and Norrie were going to play for the hosts, with Dan Evans leading the English side.
Jamie Murray said that some things are bigger than tennis.
It is disappointing for all of us that this has happened, for the players, and for the fans who wanted to watch us. Keeping everyone safe is all that matters.
The event will be held in 2022.
James Ward, a former British number two, has retired from tennis.
In Britain's opening tie against the United States in the Davis Cup, Ward beat John Isner, a top-20 player.
The Londoner was ranked 89th in the world after reaching the third round of Wimbledon in 2015, and then faced top seed Novak Djokovic at the All England Club a year later.
"From camping outside Wimbledon for a ticket at the age of 10, to go on and play the world number one on Centre Court, breaking into the Top 100 and winning the Davis Cup representing Great Britain - I can live with that," said Ward, who has struggled with knee injuries in recent
I look forward to what's next now that it's time to enjoy life in a different way.
