Maps which preserve equality of distance

Periodic Maps Which Preserve a Complex Structure

Mappings which preserve regular dodecahedrons

for all x, y ∈ X . A distance r > 0 is said to be preserved by a mapping f : X → Y if ‖ f (x)− f (y)‖ = r for all x, y ∈ X whenever ‖x− y‖ = r. If f is an isometry, then every distance r > 0 is preserved by f , and conversely. We can now raise a question whether each mapping that preserves certain distances is an isometry. Indeed, Aleksandrov [1] had raised a question whether a mapping f : X → ...

Resolvable Maps Preserve Complete Metrizability

Let X be a Polish space, Y a separable metrizable space, and f : X → Y a continuous surjection. We prove that if the image under f of every open set or every closed set is resolvable, then Y is Polish. This generalizes similar results by Sierpiński, Vainštain, and Ostrovsky.

Quasimöbius maps preserve uniform domains

We show that if a domain Ω in a geodesic metric space is quasimöbius to a uniform domain in some metric space, then Ω is also uniform. Mathematics Subject Classification (2000). 30C65

Curvature Element Transformations Which Preserve Integrable Fields.

I Shohat, J., Bull. Am. Math. Soc., 41, 51 (1935). 2 Haar, A., Math. Ann., 78, 121-136 (1918). 3 Young, W. H., Comptes Rendus, 165, 696-699 (1917). 4Szego, G., Math. Zeit., 12, 61-94 (1922). b A general treatment, which sets forth necessary and sufficient conditions for equivalence of expansions in terms of orthogonal functions, is given by Walsh, J. L., and Wiener, N., Jour. Math. and Phys. of...