Atlas: A double-cover of Heath’s V-space admitting no global section by Fred E.J. Linton

International Conference on Topology and its Applications 2007 at Kyoto (Jointly with 4th Japan Mexico Topology Conference)
December 3-7, 2007
Department of Mathematics, Kyoto University
Kyoto, Japan

Organizers
Chair: Akira Kono, Salvador Garcia-Ferreira; Algebraic Topology: Norio Iwase, Miguel A. Xicote'ncatl; Knot Theory: Akio Kawauchi, Mario Eudave; Set Theory, Set-theoretic Topology: Tsugunori Nogura, Angel Tamariz-Mascarua, Diego Rebolledo-Rojas; Geometric Topology, Continuum Theory: Hisao Kato, Sergey Antonyan; Dynamical Systems: Hiroshi Kokubu

A double-cover of Heath’s V-space admitting no global section
by
Fred E.J. Linton
Wesleyan University, Middletown, CT, USA [Emeritus]

While it would appear that it is primarily its connectedness that prevents the familiar double cover of the circle from admitting a global section, the impression that one must have connectedness for such examples to be available is illusory. To illustrate, we exhibit a double cover of Heath’s (very disconnected) V-space likewise admitting no global section. The motivation for finding such a disconnected example came from topos theory; we will present both the example and that motivation.

Date received: October 27, 2007