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Kirby's Problem List in Low-Dimensional Topol
http://www.math.berkeley.edu/~kirby/
Problems list in PostScript format.
Open Problems in Topology
http://www.franko.lviv.ua/faculty/mechmat/Departments/AlgTop/Seminars/OpenInTopology.html
Compiled by the Algebra and Topology group, Faculty of Mechanics and Mathematics, Lviv, Ukraine.
Questions in Topology
http://at.yorku.ca/topology/qintop.htm
Part of the Topology Atlas.
The Boise Problem Book
http://math.boisestate.edu/~marion/research/BoiseProblemBook/
Problems in combinatorial set theory and topology, collected by Marion Scheepers.
Thrackle.org
http://www.thrackle.org/
John Conway's Thrackle Conjecture: a compilation of what is known about the question.