OPEN PROBLEMS IN TOPOLOGY

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Toronto ProblemsAlan Dow 1Juris Steprāns 1Franklin D. Tall 1Steve Watson 1William Weiss 1There are many set-theoretic topologists and set theorists in the Municipalityof Metropolitan Toronto. We have had a seminar for 15 years or so andmost of the regular participants have been there for around a decade. Thusthe Editors thought it useful for us to compile a list of problems that interestus. This we have done in separate chapters arranged alphabetically by authorbelow.1 The authors acknowledge support from the Natural Sciences and Engeneering ResearchCouncil of Canada
Open Problems in TopologyJ. van Mill and G.M. Reed (Editors)c○ Elsevier Science Publishers B.V. (North-Holland), 1990Chapter 1Dow’s QuestionsAlan DowDept. of MathYork University4700 Keele StreetNorth York, OntarioCanada M3J 1P3dowa@clid.yorku.ca
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 12 and 13: xivContents5. Borel Selectors and M
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
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Page 28 and 29: Open Problems in TopologyJ. van Mil
Page 30 and 31: 24 Tall / Tall’s Questions [ch. 3
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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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434 Daverman / Finite-dimensional m
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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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