Two point set extensions – a counterexample. (English) Zbl 0880.54022
Summary: We show that there exist Cantor sets in the circle that are not extendable to sets that meet every line in the plane in exactly two points. This result solves a problem that was formulated by R. D. Mauldin.
MSC:
| 54G20 | Counterexamples in general topology |
References:
| [1] | R. D. Mauldin, Problems in topology arising from analysis, Open Problems in Topology, J. van Mill and G. M. Reed, eds., North-Holland, Amsterdam, 1990, pp. 617-629. CMP 91:03 |
| [2] | R. D. Mauldin, On sets which meet each line in exactly two points, in preparation. · Zbl 0931.28001 |
| [3] | J. van Mill and G. M. Reed, Open problems in topology, Topology Appl. 62 (1995), no. 1, 93 – 99. · Zbl 0811.54002 · doi:10.1016/0166-8641(94)00092-H |
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