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# Open Problems in Topology II

## 1st Edition

**Editors:**Elliott Pearl

**eBook ISBN:**9780080475295

**Hardcover ISBN:**9780444522085

**Imprint:**Elsevier Science

**Published Date:**15th March 2007

**Page Count:**776

## Description

This volume is a collection of surveys of research problems in topology and its applications. The topics covered include general topology, set-theoretic topology, continuum theory, topological algebra, dynamical systems, computational topology and functional analysis.

## Key Features

- New surveys of research problems in topology
- New perspectives on classic problems
- Representative surveys of research groups from all around the world

## Readership

Researchers and mathematicians

## Table of Contents

**Part 1. General Topology**

- Selected ordered space problems (H. Bennett and D. Lutzer)
- Problems on star-covering properties (M. Bonanzinga and M. Matveev)
- Function space topologies (D.N. Georgiou, S.D. Iliadis and F. Mynard)
- Spaces and mappings: special networks (C. Liu and Y. Tanaka)
- Extension problems of real-valued continuous functions (H. Ohta and K. Yamazaki)
- LE(k)-spaces (O. Okunev)
- Problems on (ir) resolvability (O. Pavlov)
- Topological games and Ramsey theory (M. Scheepers)
- Selection principles and special sets of reals (B. Tsaban)

**Part 2. Set-theoretic Topology** - Introduction: Twenty problems in set-theoretic topology (M. Hrusák and J.T. Moore)
- Thin-tall spaces and cardinal sequences (J. Bagaria)
- Sequential order (A. Dow)
- On D-spaces (T. Eisworth)
- The fourth head of BN (I. Farah)
- Are stratifiable spaces M1? (G. Gruenhage)
- Perfect compacta and basis problems in topology (G. Gruenhage and J.T. Moore)
- Selection problems for hyperspaces (V. Gutev and T. Nogura)
- Efimov's problem (K.P. Hart)
- Completely separable MAD families (M. Hrusák and P. Simon)
- Good, splendid and Jakovlev (I. Juhász and W.A.R. Weiss)
- Homogeneous compacta (J. van Mill)
- Compact spaces with hereditarily normal squares (J.T. Moore)
- The metrization problem for Fréchet groups (J.T. Moore and S. Todorcevic)
- Cech-Stone remainders of discrete spaces (P.J. Nyikos)
- First countable, countably compact, noncompact spaces (P.J. Nyikos)
- Linearly Lindelöf problems (E. Pearl)
- Small Dowker spaces (P.J. Szeptycki)
- Reflection of topological properties to N1 (F.D. Tall)
- The Scarborough-Stone problem (J.E. Vaughan)

**Part 3. Continuum Theory** - Questions in and out of context (D.P. Bellamy)
- An update on the elusive fixed-point property (C.L. Hagopian)
- Hyperspaces of continua (A. Ilanes)
- Inverse limits and dynamical systems (W.T. Ingram)
- Indecomposable continua (W. Lewis)
- Open problems on dendroids (V. Martínez-de-la-Vega and J.M. Martínez-Montejano)
- ½-Homogeneous continua (S.B. Nadler, Jr.)
- Thirty open problems in the theory of homogeneous continua (J.R. Prajs)

**Part 4. Topological Algebra** - Problems about the uniform structures of topological groups (A. Bouziad and J-P. Troallic)
- On some special classes of continuous maps (M.M. Clementino and D. Hofmann)
- Dense subgroups of compact groups (W.W. Comfort)
- Selected topics from the structure theory of topological groups (D. Dikranjan and D. Shakhmatov)
- Recent results and open questions relating Chu duality and Bohr compactifications of locally compact groups (J. Galindo, S. Hernández and T-S. Wu)
- Topological transformation groups: selected topics (M. Megrelishvili)
- Forty-plus annotated questions about large topological groups (V. Pestov)

**Part 5. Dynamical Systems** - Minimal flows (W.F. Basener, K. Parwani and T. Wiandt)
- The dynamics of tiling spaces (A. Clark)
- Open problems in complex dynamics and "complex" topology (R.L. Devaney)
- The topology and dynamics of flows (M.C. Sullivan)

**Part 6. Computer Science** - Computational topology (D. Blackmore and T.J. Peters)

**Part 7. Functional Analysis** - Non-smooth analysis, optimisation theory and Banach space theory (J.M. Borwein and W.B. Moors)
- Topological structures of ordinary differential equations (V.V. Filippov)
- The interplay between compact spaces and the Banach spaces of their continuous functions (P. Koszmider)
- Tightness and t-equivalence (O. Okunev)
- Topological problems in nonlinear and functional analysis (B. Ricceri)
- Twenty questions on metacompactness in function spaces (V.V. Tkachuk)

**Part 8. Dimension Theory** - Open problems in infinite-dimensional topology (T. Banakh, R. Cauty and M. Zarichnyi)
- Classical dimension theory (V.A. Chatyrko)
- Questions on weakly infinite-dimensional spaces (V.V. Fedorchuk)
- Some problems in the dimension theory of compacta (B.A. Pasynkov)

**Part 9. Invited Papers** - Problems from the Lviv topological seminar (T. Banakh, B. Bokalo, I. Guran, T. Radul and M. Zarichnyi)
- Problems from the Bizerte-Sfax-Tunis Seminar (O. Echi, H. Marzougui and E. Salhi)
- Cantor set problems (D.J. Garity and D. Repovs)
- Problems from the Galway Topology Colloquium (C. Good, A. Marsh, A. McCluskey and B. McMaster)
- The lattice of quasi-uniformities (E.P. de Jager amd H-P.A. Künzi)
- Topology in North Bay: some problems in continuum theory, dimension theory and selections (A. Karasev, M. Tuncali and V. Valov)
- Moscow questions on topological algebra (K.L. Kozlov, E.A. Reznichenko and O.V. Sipacheva)
- Some problems from George Mason University (J. Kulesza, R. Levy and M. Matveev)
- Some problems on generalized metrizable spaces (S. Lin)
- Problems from the Madrid Department of Geometry and Topology (J.M.R. Sanjurjo)
- Cardinal sequences and universal spaces (L. Soukup)

List of contributors Index

## Details

- No. of pages:
- 776

- Language:
- English

- Copyright:
- © Elsevier Science 2007

- Published:
- 15th March 2007

- Imprint:
- Elsevier Science

- eBook ISBN:
- 9780080475295

- Hardcover ISBN:
- 9780444522085

## About the Editor

### Elliott Pearl

### Affiliations and Expertise

Toronto, Canada