 This function is bijective and continuous, but not a homeomorphism (formula_26 is compact but formula_27 is not).The function formula_22 is not continuous at the point formula_29, because although formula_22 maps formula_29 to formula_32, any neighbourhood of this point also includes points that the function maps close to formula_33, but the points it maps to numbers in between lie outside the neighbourhood.Homeomorphisms are the isomorphisms in the category of topological spaces.