Introduction to Topology and Geometry. 2nd Edition. Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts
- Language: English
- 536 Pages
- Published: May 2013
The book presents surveys describing recent developments in most of the primary subfields of
General Topology and its applications to Algebra and Analysis during the last decade. It follows freely
the previous edition (North Holland, 1992), Open Problems in Topology (North Holland, 1990) and
Handbook of Set-Theoretic Topology (North Holland, 1984). The book was prepared in
connection with the Prague Topological Symposium, held in 2001. During the last 10 years the focus
in General Topology changed and therefore the selection of topics differs slightly from those
chosen in 1992. The following areas experienced significant developments: Topological Groups, Function Spaces, Dimension Theory, Hyperspaces, Selections, Geometric Topology (including
Infinite-Dimensional Topology and the Geometry of Banach Spaces). Of course, not every important topic
could be included in this book.
Except surveys, the book contains several historical essays written by such eminent topologists as:
R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L. Vietoris are added). In addition to extensive author and subject indexes, a list of all problems and questions posed in this book are added.
List of all authors of surveys:
A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D. Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G. Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J. Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P. Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
Topological invariants in algebraic environment (A.V. Arhangel'skii).
Matrices and ultrafilters (J. Baker, K. Kunen).
Recent developments in the topology of ordered spaces (H.R. Bennett, D.J. Lutzer).
Infinite-dimensional topology (J.J. Dijkstra, J. van Mill).
Recent results in set-theoretical topology (A. Dow).
Topics in topological dynamics, 1991 to 2001 (E. Glasner).
Banach spaces of continuous functions on compact spaces (G. Godefroy).
Metrizable spaces and generalizations (G. Gruenhage).
Recent progress in the topological theory of semigroups and the algebra of &bgr
S (N. Hindman, D. Strauss).
Recent progress in hyperspace topologies (L'. Holá, J. Pelant).
Some topics in geometric topology (K. Kawamura).
Quasi-uniform spaces in the year 2001 (H.-P. Künzi).
Function spaces (W. Marciszewski).
Topology and domain theory (K. Martin, M.W. Mislove, G.M. Reed).
Topics in dimension theory (R. Pol, H. Toruñczyk).
Continuous selections of multivalued mappings (D. Repovŝ, P.V. Semenov).
Convergence in the presence of algebraic structure (D. Shakhmatov).
Descriptive set theory in topology (S. Solecki).
Topological groups: between compactness and ℵo-boundedness (M. Tkachenko).
Essays (R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardeŝić, J. Nagata, M.E. Rudin, Yu.M. Smirnov, reminiscences of L. Vietoris).
List of open problems and questions.
van Mill, J.