A double-cover of Heath’s V-space admitting no global section
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.

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