Kai, a 62,500 square-foot ‘water culture house’ with 10 indoor and outdoor pools, will open on December 5.

Rasmus Hjortshøj

Copenhagen is a swimmer’s city. "The cure for anything is salt water: sweat, tears, or the sea," Danish author Karen Blixen, who lived up the coast from Copenhagen, famously wrote in 1934. Locals and visitors alike have taken her words to heart ever since.

In the early 2000s, floating swimming pools were introduced to the Danish capital's harbor after the city's shipbuilding industry collapsed. These pools turned an unused space into a playground for swimmers, divers, water polo enthusiasts, and boaters, especially on hot summer days .…