Contents 1. Introduction .................................................................................................. 5 2. Antoine's necklaces.................................................................................... 6 3. Wreaths......................................................................................................... 7 4. Construction of discs.................................................................................. 7 5. Construction of Bing-Borsuk retracts ..................................................... 9 6. Sets in solid tori ......................................................................................... 10 7. Replacing discs in solid tori .................................................................... 14 8. Discs in $X^{ir}$.......................................................................................... 18 9. $X^{ir}$ is an AR.......................................................................................... 19 10. Construction of the decomposition M................................................... 22 11. X is a 2-dimensional AR.......................................................................... 30 12. Q* contains a 2-dimensional AR........................................................... 36 13. Concluding remarks ............................................................................... 36 References ...................................................................................................... 39