On convex bodies of constant width
Abstract We present an alternative proof of the following fact: the hyperspace of compact closed subsets of constant width in R n is a contractible Hilbert cube manifold. The proof also works for certain subspaces of compact convex sets of constant width as well as for the pairs of compact convex sets of constant relative width. Besides, it is proved that the projection map of compact closed subsets of constant width is not 0-soft in the sense of Shchepin, in particular, is not open.
Lectures on Hilbert Cube Manifolds
Preliminaries Z-sets in Q Stability of Q-manifoldsitle> Z-sets in Q-manifolds Q-manifolds of the form $M \times [0, 1)$ Shapes of Z-sets in Q Near homeomorphisms and the Sum Theorem Applications of the Sum Theorem The Splitting Theorem The Handle Straightening Theorem The Triangulation Theorem The Classification Theorem Cell-like mappings The ANR Theorem References Appendix Open problems in infinite-dimensional topology.
The genus Pseudolithophyllum (Corallinaceae) in the Gulf of Maine
SummaryThis is the third of a series of papers covering the anatomy, morphology, systematics and ecology of the crustose corallines of the Gulf of Maine. Pseudolithophyllum orbiculatum, the only species of this genus in the region, is treated in this paper.