OPEN PROBLEMS IN TOPOLOGY

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xivContents5. Borel Selectors and Matchings . . . . . . . . . . . . . . . . . . . . . 6236. Dynamical Systems on S 1 × R—Invariant Continua . . . . . . . . . 6247. Borel Cross-Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . 627References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 627VIII Dynamics 631Continuum Theory and Topological Dynamicsby M. Barge and J. Kennedy . . . . . . . . . . . . . . . . . . . . . . . 633One-dimensional versus two-dimensional dynamicsby S. van Strien . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6451. The existence of periodic points . . . . . . . . . . . . . . . . . . . . 6472. The boundary of ‘chaos’ . . . . . . . . . . . . . . . . . . . . . . . . . 6483. Finitely many sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . 6504. Homeomorphisms of the plane . . . . . . . . . . . . . . . . . . . . . 6515.Mapsoftheannulus...........................652References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652Index of general terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655Index of terms used in the problems . . . . . . . . . . . . . . . . . . . . . 673
Part ISet Theoretic TopologyContents:Dow’s Questionsby A. Dow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5Steprāns’ Problemsby J. Steprans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Tall’s Problemsby F. D. Tall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21Problems I wish I could solveby S. Watson ................................ 37Weiss’ Questionsby W. Weiss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Perfectly normal compacta, cosmic spaces, and some partition problemsby G. Gruenhage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85Open Problems on βωby K. P. Hart and J. van Mill ...................... 97On first countable, countably compact spaces III: The problem of obtainingseparable noncompact examplesby P. Nyikos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Set-theoretic problems in Moore spacesby G. M. Reed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163Some Conjecturesby M. E. Rudin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183Small Uncountable Cardinals and Topologyby J. E. Vaughan. With an Appendix by S. Shelah . . . . . . . . . . 195
Page 1: OPEN PROBLEMSIN TOPOLOGYEdited byJa
Page 4 and 5: viIntroductionThe editors would lik
Page 6 and 7: viiiContents10. Homeomorphisms . .
Page 8 and 9: xContentsSome Open Problems in Dens
Page 10 and 11: xiiContentsConclusion and Open Prob
Page 14 and 15: Toronto ProblemsAlan Dow 1Juris Ste
Page 16 and 17: Question 1. Is there a ccc non-pseu
Page 18 and 19: ch. 1] Dow / Dow’s Questions 9Thi
Page 20 and 21: References 11[1990] The space of mi
Page 22 and 23: 1. The Toronto ProblemWhat has come
Page 24 and 25: §3] Autohomeomorphisms of the Čec
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Page 28 and 29: Open Problems in TopologyJ. van Mil
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Page 42 and 43: Open Problems in TopologyJ. van Mil
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60 Watson / Wishes [ch. 4? 136.Prob
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62 Watson / Wishes [ch. 4Problem 78
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64 Watson / Wishes [ch. 4van Rooij
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66 Watson / Wishes [ch. 4In the not
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68 Watson / Wishes [ch. 413. Other
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70 Watson / Wishes [ch. 4Bales, J.
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72 Watson / Wishes [ch. 4[1978] Sep
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74 Watson / Wishes [ch. 4Reed, G. M
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76 Watson / Wishes [ch. 4[19∞b] A
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What constitutes a good mathematica
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§C] Problems about Partitions 81Ea
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References 83It is known that the a
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Open Problems in TopologyJ. van Mil
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88 Gruenhage / Perfectly normal com
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100 Hart and van Mill / βω [ch. 7
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130 Nyikos / Countably compact spac
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166 Reed / Moore Spaces [ch. 9? 298
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168 Reed / Moore Spaces [ch. 9? 302
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170 Reed / Moore Spaces [ch. 9Reed
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172 Reed / Moore Spaces [ch. 9An ex
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174 Reed / Moore Spaces [ch. 96. Th
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176 Reed / Moore Spaces [ch. 98. Re
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178 Reed / Moore Spaces [ch. 9van D
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180 Reed / Moore Spaces [ch. 9[1975
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186 Rudin / Some Conjectures [ch. 1
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198 Vaughan / Small Cardinals [ch.
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224 Bennett and Chaber / The Class
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234 Bennett and Lutzer / Perfect Or
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236 Bennett and Lutzer / Perfect Or
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IntroductionIt is the purpose of th
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§1] Origins 241Then there is a met
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§2] The point-countable base probl
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§2] The point-countable base probl
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§3] Postscript: a general structur
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References 249However, we do not kn
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254 Fitzpatrick and Zhou / Densely
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264 Kunen / Large Homogeneous Compa
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0. IntroductionThis note collects s
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§3] Continuous selections 2752.3.
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References 277metric satisfying bot
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282 Pol / Dimension Theory [ch. 18T
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284 Pol / Dimension Theory [ch. 18W
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286 Pol / Dimension Theory [ch. 18I
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288 Pol / Dimension Theory [ch. 181
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290 Pol / Dimension Theory [ch. 18G
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Part IIIContinua TheoryContents:Ele
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Most of the topics related to conti
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ch. 19] Cook, Ingram and Lelek / Co
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References 301questions related to
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306 Rogers / Tree-like curves [ch.
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316 Comfort / Topological Groups [c
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352 Lawson and Mislove / Domain The
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378 Kong et al / Binary Digital Ima
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390 Meyer and de Vink / Semantics [
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412 Dobrowolski and Mogilski / Inco
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460 Dydak and Segal / Shape Theory
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472 Carlsson / Algebraic Topology [
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0. IntroductionThis paper is an int
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§1] Reidemeister Moves, Special Mo
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§2] Knotted Strings? 493embedding
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§3] Detecting Knottedness 495(Thus
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§4] Knots and Four Colors 4974. Kn
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§5] The Potts Model 499 GK(G)Figu
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§6] States, Crystals and the Funda
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§7] Vacuum-Vacuum Expectation and
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§8] Spin-Networks and Abstract Ten
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§9] Colors Again 5119.1. Theorem (
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§9] Colors Again 513At an edge in
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§10] Formations 515Ì ÍFigure 9:
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§11] Mirror-Mirror 517−−−→
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References 519Burgoyne, P. N.[1963]
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References 521Kirby, R.[1978] A cal
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526 West / Infinite Dimensional Top
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Part VIITopology Arising from Analy
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By a space we mean a Tikhonov topol
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ch. 31] Arkhangel ′ ski / C p -th
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References 613ReferencesArkhangel
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References 615Sokolov, G. A.[1986]
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1. Topologically Equivalent Measure
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§2] Two-Point Sets 621Brouwer’s
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§4] Finite Shift Maximal Sequences
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§6] Dynamical Systems on S 1 × R
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References 6277. Borel Cross-Sectio
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References 629Navarro-Bermudez, F.
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636 Barge and Kennedy / Continua an
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In this note I want to pose some qu
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§2] The boundary of ‘chaos’ 64
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§4] Homeomorphisms of the plane 65
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References 653Boyland, P.[1987] Bra
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Index of general termsThe index is
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Index of general terms 657bordism,
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Index of general terms 659continuou
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Index of general terms 661free surf
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Index of general terms 663linear sp
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Index of general terms 665Pacman, 1
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Index of general terms 667sequentia
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Index of general terms 669paracompa
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Index of general terms 671unconditi
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674 Index of problem termscharacter
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676 Index of problem termshereditar
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678 Index of problem termssimple, 4
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680 Index of problem termscontracti
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682 Index of problem termsLC 1 comp
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684 Index of problem termsproduct w
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686 Index of problem termsPL standa
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688 Index of problem termsstrongly
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690 Index of problem termsU α-univ
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692 Index of problem termson uncoun
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