Hmm, I'm thinking about say 60,000rpm or 10,000 rps with a 3 metre
diameter fan.(Making these numbers up but I expect they are in the
ballpark) therefore the tip is travelling approx 9m * 10,000m every
second or 36km/sec or 1500km/hr or about mach1.2?

That's in stationary air - ignoring any advancing blade scenario.

My guess is that because the tips are enclosed inside a duct that there
is no vortex or boundary effects at the tips?

D'oh! Only 1000 rps!

Yeah, you were thinking of the inner stages. Your RPM range of ten
thousands is realistic on the inner shaft for last compressor and first
turbine stages. Their diameters are below 0.5m. The outer stages get
bigger and have lower RPM. For the fans there might even be a gear.

The border between (turbo)propeller and (turbo)fan is quite fluent.

But an interesting question is why nobody ever tried a supersonic rotor.
Maybe it's easier to fold or stop the rotor than to make it strong
enough and still efficient for sub- and supersonic speeds.