Electronic Version 16 (1991), 89-93

W. T. Ingram

In the American Journal of Mathematics in 1959, M. K. Fort wrote a beautiful paper in which he proved that the dyadic solenoid is not a continuous image of any plane continuum. In that paper he also showed that a certain spiral to two circles is not a continuous image of any non-separating plane continuum. These results relied on a theorem of Morton Curtis on locally trivial fibre spaces with totally disconnected fibres. The author has always found these arguments somewhat less than satisfying because, in particular, they cannot be used to show that a spiral to a single circle is not a continuous image of any non-separating plane continuum. In this paper, we isolate a theorem from which all these results can be obtained. Specifically, this theorem avoids the use of the results on locally trivial fibre spaces.

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volume 16: table of contents
topology proceedings Electronic Version