There do exist spaces X that are subsets of the plane possessing a continuous bijection X —> X without continuous inverse. Consider it a puzzle if you like. (But not the Klein bottle.) —Dan Bill Gosper wrote: ----- DanA: Consider the space Homeo(K) of self-homeomorphisms of the Klein bottle. I.e., Homeo(K) consists of all continuous bijections h : K —> K having a continuous inverse. __________ Umm, can somebody show me a continuous bijection with a *dis*continuous inverse? -----