Bundle Map Theory in the Category of Weak Hausdorff K-spaces

We generalize Theorem 2.1 of H.Oshima and K. Tsukiyama [12] and prove Theorem 2.3 of I. M. James [7] without his condition. We identify the boundary homomorphism of the homotopy exact sequence of the evaluation fibration with the generalized Whitehead product. The new point is that we work not in the category of CW-complexes but in the category of well based weak Hausdorff k-spaces.