For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option

https://tysonltye150.swiftnestly.com/posts/what-to-know-before-replacing-an-ac-system-in-salt-lake-city-2

For Salt Lake City homes with no ductwork, ductless mini-split heat pumps are a recognized option, especially where existing heating is radiant, hydronic, or space-heater based.