Abstract
The following observations, more gossip than history, are concerned with some of the topologists whom I encountered and who influenced me in the 1940s (and a little earlier). In those days the distinction between “general” and “algebraic” or “combinatorial” topology was less rigid than now, and many mathematicians were interested in both—Alexander and Hurewicz, for example. So I shall not always try to maintain this distinction.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J.W. Alexander, Ordered sets, complexes and the problem of compactification, Proc. Nat. Acad. Sci. 24 (1939) 296–298.
P. Alexandroff and H. Hopf, Topologie (vol. I), Springer (Berlin) 1935.
W.L. Ayres, A new proof of the cyclic connectivity theorem, Bull. Amer. Math. Soc. 48 (1942) 627–630.
N. Bruschlinsky, Stetige Abbildungen und Bettische Gruppen der Dimensionszahlen 1 und 3, Math. Annalen 109 (1934), 525–537.
H. Cartan, Théorie des filtres, Comptes Rendus Paris 205 (1937) 595–598.
Filtres et ultrafiltres, Comptes Rendus Paris 205 (1937) 777–779.
C. Chevalley and O. Frink, Jr., Bicompactness of Cartesian products, Bull. Amer. Math. Soc. 47 (1941) 612–614.
J. Dieudonné, Une généralization des espaces compacts, J. Math. Pures Appl. 23 (1944) 65–71.
C.H. Dowker, Hopf’s Theorem for non-compact spaces, Proc. Nat. Acad. Sci. 23 (1937) 293–294.
C.H. Dowker, Mapping theorems for non-compact spaces, Amer. J. Math. 69 (1947) 200–242.
C.H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951) 219–224.
S. Eilenberg, Transformations continues en circonférence et la topologie du plan, Fund. Math. 26 (1936) 61–112.
S. Eilenberg, Sur les espaces multicohérents I, Fund. Math. 27 (1936) 153–190.
P. Erdös and A.H. Stone, Some remarks on almost periodic transformations, Bull. Amer. Math. Soc. 51 (1945) 126–130.
P. Erdös and A.H. Stone, On the structure of linear graphs, Bull. Amer. Math. Soc. 52 (1946) 1087–1091.
R. Fox, On topologies for function spaces, Bull. Amer. Math. Soc. 51 (1945) 429–432.
W. Hurewicz and H. Wallman, Dimension Theory, Princeton 1941.
J.L. Kelley, Convergence in topology, Duke Math. J. 17 (1950) 277–283.
S. Lefschetz, Topics in topology, Ann. of Math. Studies 10, Princeton 1942.
M.H.A. Newman, Elements of the Topology of Plane Sets of Points, Cambridge University Press 1939 (second edition 1951 ).
A.H. Stone, Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948) 977–982.
A.H. Stone and J.W. Tukey, Generalized “sandwich” theorems, Duke Math. J. 9 (1942) 356–359.
J.W. Tukey, Convergence and uniformity in topology, Ann. of Math. Studies 2, Princeton 1940.
A.D. Wallace, Separation spaces, Ann. of Math. (2) 42 (1941) 687–697.
H. Wallman, Lattices and topological spaces, Ann. of Math. (2) 39 (1938) 112–126.
A.J. Ward, The topological characterization of an open interval, Proc. London Math. Soc. (2) 41 (1936) 191–198.
A. Weil, Sur les espaces à structure uniforme et sur la topologie générale,Act. Scient. Ind. 551, Hermann, Paris, 1937–38.
G. Whyburn, Analytic Topology, Amer. Math. Soc. Colloquium Publications 28, New York 1942.
R.L. Wilder, Topology of Manifolds, Amer. Math. Soc. Colloquium Publications 32, New York 1949.
G.S. Young, Jr., The introduction of local connectivity by change of topology, Amer. J. Math 68 (1946) 479–494.
G.S. Young, A characterization of 2-manifolds, Duke Math. J. 14 (1947) 979–990.
J.W.T. Youngs, K-cyclic elements, Amer. J. Math. 62 (1940) 449–456.
M. Zorn, A remark on method in transfinite algebra, Bull. Amer. Math. Soc. 41 (1935) 667–670.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Stone, A.H. (1997). Some Topologists of the 1940s. In: Aull, C.E., Lowen, R. (eds) Handbook of the History of General Topology. History of Topology, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0468-7_9
Download citation
DOI: https://doi.org/10.1007/978-94-017-0468-7_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4820-2
Online ISBN: 978-94-017-0468-7
eBook Packages: Springer Book Archive