Book Review
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MathSciNet review:
1566913
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Book Information:
Author:
Maurice D. Weir
Title:
Hewitt-Nachbin spaces
Additional book information:
North-Holland/American Elsevier, Amsterdam, 1975, 270 + vii pp., $15.50.
1. P. Alexandroff and P. Urysohn, Mémoire sur les espaces topologiques compacts, Verh. Kon. Akad. Vetensch. Amsterdam 14 (1929), 1-96.
Jean Bénabou, Critères de représentabilité des foncteurs, C. R. Acad. Sci. Paris 260 (1965), 752–755 (French). MR 175946
Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), no. 4, 823–844. MR 1503374, DOI 10.2307/1968839
Paul J. Cohen, Set theory and the continuum hypothesis, W. A. Benjamin, Inc., New York-Amsterdam, 1966. MR 0232676
W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Die Grundlehren der mathematischen Wissenschaften, Band 211, Springer-Verlag, New York-Heidelberg, 1974. MR 0396267
J. N. Crossley, C. J. Ash, C. J. Brickhill, J. C. Stillwell, and N. H. Williams, What is mathematical logic?, Oxford Paperbacks University Series, No. 60, Oxford University Press, London-New York, 1972. MR 0414308
7. Frank R. Drake, Set theory: An introduction to large cardinals, North-Holland, Amsterdam, 1974.
R. Engelking, Outline of general topology, North-Holland Publishing Co., Amsterdam; PWN—Polish Scientific Publishers, Warsaw; Interscience Publishers Division John Wiley & Sons, Inc., New York, 1968. Translated from the Polish by K. Sieklucki. MR 0230273
R. Engelking and S. Mrówka, On $E$-compact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 429–436. MR 0097042
10. Peter J. Freyd, Functor theory, Ph. D. Dissertation, Princeton Univ., 1960.
Peter Freyd, Abelian categories. An introduction to the theory of functors, Harper’s Series in Modern Mathematics, Harper & Row, Publishers, New York, 1964. MR 0166240
12. Leonard Gillman, Real-compact spaces (Q-spaces), Bull. Amer. Math. Soc. 63 (1957), 144-145 (Abstract).
Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199
Irving Glicksberg, Stone-Čech compactifications of products, Trans. Amer. Math. Soc. 90 (1959), 369–382. MR 105667, DOI 10.1090/S0002-9947-1959-0105667-4
Horst Herrlich, ${\mathfrak {E}}$-kompakte Räume, Math. Z. 96 (1967), 228–255 (German). MR 205218, DOI 10.1007/BF01124082
Horst Herrlich, On the concept of reflections in general topology, Contributions to Extension Theory of Topological Structures (Proc. Sympos., Berlin, 1967) Deutscher Verlag Wissensch., Berlin, 1969, pp. 105–114. MR 0284986
H. Herrlich and J. van der Slot, Properties which are closely related to compactness, Nederl. Akad. Wetensch. Proc. Ser. A 70=Indag. Math. 29 (1967), 524–529. MR 0222848
Edwin Hewitt, Rings of real-valued continuous functions. I, Trans. Amer. Math. Soc. 64 (1948), 45–99. MR 26239, DOI 10.1090/S0002-9947-1948-0026239-9
Edwin Hewitt, Linear functionals on spaces of continuous functions, Fund. Math. 37 (1950), 161–189. MR 42684, DOI 10.4064/fm-37-1-161-189
M. Hušek, Hewitt realcompactification of products, Topics in topology (Proc. Colloq., Keszthely, 1972) Colloq. Math. Soc. János Bolyai, Vol. 8, North-Holland, Amsterdam, 1974, pp. 427–435. MR 0372825
Daniel M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294–329. MR 131451, DOI 10.1090/S0002-9947-1958-0131451-0
J. F. Kennison, Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303–315. MR 174611, DOI 10.1090/S0002-9947-1965-0174611-9
23. F. William Lawvere, Functorial semantics of algebraic theories (with appendix), Ph. D. Dissertation, Columbia Univ., 1963.
Edgar R. Lorch, Compactification, Baire functions, and Daniell integration, Acta Sci. Math. (Szeged) 24 (1963), 204–218. MR 163281
George W. Mackey, Equivalence of a problem in measure theory to a problem in the theory of vector lattices, Bull. Amer. Math. Soc. 50 (1944), 719–722. MR 10782, DOI 10.1090/S0002-9904-1944-08220-7
Barry Mitchell, Theory of categories, Pure and Applied Mathematics, Vol. XVII, Academic Press, New York-London, 1965. MR 0202787
S. Mrówka, On the unions of $Q$-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 6 (1958), 365–368. MR 0102786
S. Mrówka, Some comments on the author’s example of a non-${\cal R}$-compact space, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 443–448 (English, with Russian summary). MR 268852
S. Mrówka, Recent results on $E$-compact spaces and structures of continuous functions, Proceedings of the University of Oklahoma Topology Conference Dedicated to Robert Lee Moore (Norman, Okla., 1972) Univ. of Oklahoma, Norman, Okla., 1972, pp. 168–221. MR 0358693
30. Léopoldo Nachbin, Unpublished notes.
31. Léopoldo Nachbin, On the continuity of positive linear transformations, Proc. 1950 Internat. Congress of Mathematicians, Vol. I, Amer. Math. Soc., Providence, R. I., 1952, pp. 464-465.
Leopoldo Nachbin, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 471–474. MR 63647, DOI 10.1073/pnas.40.6.471
Stelios Negrepontis, Baire sets in topological spaces, Arch. Math. (Basel) 18 (1967), 603–608. MR 220248, DOI 10.1007/BF01898869
Taira Shirota, A class of topological spaces, Osaka Math. J. 4 (1952), 23–40. MR 50872
Taira Shirota, On locally convex vector spaces of continuous functions, Proc. Japan Acad. 30 (1954), 294–298. MR 64389
J. van der Slot, Universal topological properties, Math. Centrum Amsterdam Afd. Zuivere Wisk. 1966 (1966), no. ZW-011, 9. MR 242123
M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), no. 3, 375–481. MR 1501905, DOI 10.1090/S0002-9947-1937-1501905-7
A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), no. 1, 544–561 (German). MR 1512595, DOI 10.1007/BF01782364
Russell C. Walker, The Stone-Čech compactification, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 83, Springer-Verlag, New York-Berlin, 1974. MR 0380698
- 1.
- P. Alexandroff and P. Urysohn, Mémoire sur les espaces topologiques compacts, Verh. Kon. Akad. Vetensch. Amsterdam 14 (1929), 1-96.
- 2.
- Jean Bénabou, Criteres de représentabilité des foncteurs, C. R. Acad. Sci. Paris 260 (1965), 752-755. MR 31 #222. MR 0175946
- 3.
- Eduard Čech, On bicompact spaces, Ann. of Math. (2) 38 (1937), 823-844. MR 1503374
- 4.
- Paul J. Cohen, Set theory and the continuum hypothesis, Benjamin, New York and Amsterdam, 1966. MR 38 #999. MR 232676
- 5.
- W. W. Comfort and S. Negrepontis, The theory of ultrafilters, Grundlehren math. Wiss., Band 211, Springer-Verlag, Berlin and New York, 1974. MR 396267
- 6.
- J. N. Crossley, What is mathematical logic?, Oxford Univ. Press, London and New York, 1972. MR 414308
- 7.
- Frank R. Drake, Set theory: An introduction to large cardinals, North-Holland, Amsterdam, 1974.
- 8.
- R. Engelking, Outline of general topology, PWN, Warsaw, 1965; English transl., North-Holland, Amsterdam; PWN, Warsaw; Interscience, New York, 1968. MR 36 #4508; 37 #5836. MR 230273
- 9.
- R. Engelking and S. Mrówka, On E-compact spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 6 (1958), 429-436. MR 20 #3522. MR 97042
- 10.
- Peter J. Freyd, Functor theory, Ph. D. Dissertation, Princeton Univ., 1960.
- 11.
- Peter J. Freyd, Abelian categories: An introduction to the theory of functors, Harper and Row, New York, 1964. MR 29 #3517. MR 166240
- 12.
- Leonard Gillman, Real-compact spaces (Q-spaces), Bull. Amer. Math. Soc. 63 (1957), 144-145 (Abstract).
- 13.
- Leonard Gillman and Meyer Jerison, Rings of continuous functions, Van Nostrand, Princeton, N. J., 1960. MR 22 #6994. MR 116199
- 14.
- Irving Glicksberg, Stone-Čech compactifications of products, Trans. Amer. Math. Soc. 90 (1959), 369-382. MR 21 #4405. MR 105667
- 15.
- Horst Herrlich, ${\germ E}$-kompakte Räume, Math. Z. 96 (1967), 228-255. MR 34 #5051. MR 205218
- 16.
- Horst Herrlich, On the concept of reflections in general topology, Contributions to Extension Theory of Topological Structures (Proc. Sympos., Berlin, 1967), VEB Deutsch. Verlag Wissensch., Berlin, 1969, pp. 105-114. MR 44 #2210. MR 284986
- 17.
- H. Herrlich and J. van der Slot, Properties which are closely related to compactness, Nederl. Akad. Wetensch. Proc. Ser. A 70 = Indag. Math. 29 (1967), 524-529. MR 36 #5898. MR 222848
- 18.
- Edwin Hewitt, Rings of real-valued continuous functions I, Trans. Amer. Math. Soc. 64 (1948), 45-99. MR 10, 126. MR 26239
- 19.
- Edwin Hewitt, Linear functional on spaces of continuous functions, Fund. Math. 37 (1950), 161-189. MR 13, 147. MR 42684
- 20.
- M. Hušek, Hewitt realcompactification of products, Topics in Topology (Proc. Colloq., Keszthely, 1972), Colloq. Math. Soc. János Bolyai, Vol. 8, North-Holland, Amsterdam, 1974, pp. 427-435. MR 51 #9029. MR 372825
- 21.
- Daniel M. Kan, Adjoint functors, Trans. Amer. Math. Soc. 87 (1958), 294-329. MR 24 #A1301. MR 131451
- 22.
- J. F. Kennison, Reflective functors in general topology and elsewhere, Trans. Amer. Math. Soc. 118 (1965), 303-315. MR 30 #4812. MR 174611
- 23.
- F. William Lawvere, Functorial semantics of algebraic theories (with appendix), Ph. D. Dissertation, Columbia Univ., 1963.
- 24.
- E. R. Lorch, Compactification, Baire functions and Daniell integration, Acta Sci. Math. (Szeged) 24 (1963), 204-218. MR 29 #584. MR 163281
- 25.
- George W. Mackey, Equivalence of a problem in measure theory to a problem in the theory of vector lattices, Bull. Amer. Math. Soc. 50 (1944), 719-722. MR 6, 70. MR 10782
- 26.
- Barry Mitchell, Theory of categories, Academic Press, New York and London, 1965. MR 34 #2647. MR 202787
- 27.
- S. Mrówka, On the unions of Q-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 6 (1958), 365-368. MR 21 #1572. MR 102786
- 28.
- S. Mrówka, Some comments on the author's example of a non-R-compact space, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 18 (1970), 443-448. MR 42 #3749. MR 268852
- 29.
- S. Mrówka, Recent results on E-compact spaces and structures of continuous functions, Proc. Univ. Oklahoma Topology Conf. (1972), Univ. of Oklahoma, Norman, 1972, pp. 168-221. MR 50 #11152. MR 358693
- 30.
- Léopoldo Nachbin, Unpublished notes.
- 31.
- Léopoldo Nachbin, On the continuity of positive linear transformations, Proc. 1950 Internat. Congress of Mathematicians, Vol. I, Amer. Math. Soc., Providence, R. I., 1952, pp. 464-465.
- 32.
- Léopoldo Nachbin, Topological vector spaces of continuous functions, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 471-474. MR 16, 156. MR 63647
- 33.
- S. Negrepontis, Baire sets in topological spaces, Arch. Math. (Basel) 18 (1967), 603-608. MR 36 #3314. MR 220248
- 34.
- Taira Shirota, A class of topological spaces, Osaka Math. J. 4 (1952), 23-40. MR 14, 395. MR 50872
- 35.
- Taira Shirota, On locally convex vector spaces of continuous functions, Proc. Japan Acad. (= Proc. Imperial Acad., Tokyo) 30 (1954), 294-298. MR 16, 275. MR 64389
- 36.
- J. van der Slot, Universal topological properties, Math. Centrum Amsterdam Afd. Zuivere Wisk. 1966, ZW-011. MR 39 #3457. MR 242123
- 37.
- M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc. 41 (1937), 375-481. MR 1501905
- 38.
- A. Tychonoff, Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930), 544-561. MR 1512595
- 39.
- Russell C. Walker, The Stone-Čech compactification, Ergebnisse math. Grenzgebiete, vol. 83, Springer-Verlag, New York and Berlin, 1974. MR 380698
Review Information:
Reviewer:
W. W. Comfort
Journal:
Bull. Amer. Math. Soc.
82 (1976), 857-863
DOI:
https://doi.org/10.1090/S0002-9904-1976-14182-1
