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Book Review
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Book Information
Author(s):
J.~A.~Baars and J.~A.~M.~de~Groot
Title:
On topological and linear equivalence of certain function spaces
Additional book information:
CWI Tract {86}, Centrum Wisk. Inform., Amsterdam, 1992, 201 pp., DFL 60.00. ISBN 90 6196 411 3
References:
- [1]
- A. V. Arhangelskii, On linear homeomorphisms of function spaces, Soviet Math. Dokl. \textbf{25} (1982), 852--855.
- [2]
- A. V. Arhangelskii, A survey of $C_p$-theory, Questions Answers Gen. Topology \textbf{5} (1987), 1--109.
- [3]
- K.-D. Bierstedt, J. Bonet, and J. Schmets, \RM {(DF)}-spaces of type $CB(X, E)$ and $\overline {CV}(X,E)$, Note Mat. {\bf X} Suppl. 1 (1990), 127--148.
- [4]
- C. Bessaga and A. Pelczynski, \emph{Selected topics in infinite-dimensional topology}, PWN, Warszawa, 1975.
- [5]
- R. Cauty, T. Dobrowolski, and W. Marciszewski, A contribution to the topological classification of the spaces $C_p(X)$, Fund. Math. \textbf{142} (1993), 269--301.
- [6]
- L. Gilman and M. Jerison, \emph{Rings of continuous functions}, Van Nostrand, Princeton, NJ, 1960.
- [7]
- J. A. Guthrie, Ascoli theorems and the pseudocharacter of mapping spaces, Bull. Austral. Math. Soc. \textbf{10} (1974), 403--408.
- [8]
- S. V. Kislyakov, Classification of spaces of continuous functions of ordinals, Siberian Math. J. \textbf{16} (1975), 226--231.
- [9]
- L. Nachbin, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci. U.S.A. \textbf{40} (1954), 471--474.
- [10]
- J. Nagata, On lattices of functions on topological spaces and functions on uniform spaces, Osaka Math. J. \textbf{1} (1949), 166--181.
- [11]
- M. A. Naimark, Normed rings, Noordhoff, Groningen, 1959.
- [12]
- V. G. Pestov, The coincidence of the dimension $\dim $ of $l$-equivalent topological spaces, Soviet Math. Dokl. \textbf{26} (1982), 380--383.
- [13]
- J. Schmets, \emph{Espaces de fonctions continues}, Springer, Berlin, 1976.
- [14]
- J. Schmets, \emph{Spaces of vector-valued continuous functions}, Springer, Berlin, 1983.
- [15]
- Z. Semadeni, \emph{Banach spaces of continuous functions}, PWN, Warszawa, 1971.
- [16]
- T. Shirota, On locally convex vector spaces of continuous functions, Proc. Japan Acad. \textbf{30} (1954), 294--298.
- [17]
- S. Warner, The topology of compact convergence on continuous function spaces, Duke Math. J. \textbf{25} (1958), 265--282.
Additional Information:
Reviewer(s):
J.
Schmets
Review Information:
Journal:
Bull. Amer. Math. Soc.
30
(1994),
315-318.
DOI:
10.1090/S0273-0979-1994-00477-X
PII:
S 0273-0979(1994)00477-X
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