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Let X and Y be locally compact Hausdorff spaces. We give a full description of disjointness preserving Fredholm linear operators T from C0(X) into C0(Y), and show that is continuous if either Y contains no isolated point or T has closed range. Our task is achieved by writing T as a weighted composition operator Tf = h f . Through the relative homeomorphism , the structure of the range space of T can be completely analyzed, and X and Y are homeomorphic after removing finite subsets.

We define type A, type B, type C as well as C*-semi-finite C*-algebras.

Let <i>M</i> be a compact connected (topological) manifold of finite- or infinite-dimension <i>n</i>. Let 0 <i>r</i> 1 be arbitrary but fixed. We construct in this paper a space-filling curve <i>f</i> from [0,1] onto <i>M</i>, under which <i>M</i> is the image of a compact set <i>A</i> of Hausdorff dimension <i>r</i>. Moreover, the restriction of f to <i>A</i> is one-to-one over the image of a dense subset provided that 0 <i>r</i> log|2^<i>n</i>/log(2^<i>n</i> + 2). The proof is based on the special case where <i>M</i> is the Hilbert cube [0,1].

In this paper, using the concept of attractive points of a nonlinear mapping, we obtain a strong convergence theorem of Halperns type [<i>Bull. Amer. Math. Soc</i>. <b>73</b> (1967), 957961] for a wide class of nonlinear mappings which contains nonexpansive mappings, nonspreading mappings and hybrid mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems of Halperns type in a Hilbert space. In particular, we solve a problem posed by Kurokawa and Takahashi [<i>Nonlinear Anal</i>. <b>73</b> (2010, 15621568].