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n-ANR's for Certain Normal Spaces

Published online by Cambridge University Press:  20 November 2018

Vincent J. Mancuso
Vincent J. Mancuso*
Affiliation:
St. John's University
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For various classes Q of metric spaces, there are several well-known results characterizing the local n-connectivity of a metric space in terms of n-ANR(Q)'s. Specifically, we have in mind the results of Kuratowski (13, p. 265) and Kodama (10, p. 79). The main purpose of this paper will be to obtain similar results along these lines for non-metric classes Q. In the last part of the paper we specify Q to be the class of totally normal spaces and characterize the local n-connectivity of an n-dimensional separable metric space in terms of ANR(Q)'s.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 19 , 1967 , pp. 629 - 635
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Arens, R., Extension of functions on fully normal spaces, Pacific J. Math., 2 (1951), 11–22.Google Scholar
2. Bursuk, K., Sur un espace compact localement contractile qui n'est pas un rétracte absolu de voisinage, Fund. Math., 35 (1948), 175–180.Google Scholar
3. Čech, E., Contribution à la theorie de la dimension, Cas. Mat. Fys., 62 (1933), 277–291.Google Scholar
4. Dowker, C. H., Inductive dimension of completely normal spaces, Quart. J. Math., 4 (1953), 267–281.Google Scholar
5. Dowker, C. H., On a theorem of Banner, Ark. Mat., 2 (1952-54), 307–313.Google Scholar
6. Hanner, O., Retraction and extension of mappings of metric and non-metric spaces, Ark. Mat., 2 (1952-54), 315–360.Google Scholar
7. Hanner, O., Solid spaces and absolute retracts, Ark. Mat., 1 (1949-52), 375–382.Google Scholar
8. Iseki, K., On a property of mappings of metric spaces, Proc. Japan Acad., 30 (1954), 570- 571.Google Scholar
9. Katĕtov, M., On the dimension of non-separable spaces, II, Czechoslovak Math. J., 6 (1956), 485–516.Google Scholar
10. Kodama, Y., On LCn metric spaces, Prov. Japan Acad., 33 (1957), 79–83.Google Scholar
11. Kuratowski, C., Quelques problèmes concernant les espaces métriques non séparables, Fund. Math., 25 (9935), 534–545.Google Scholar
12. Kuratowski, C., Topologie I (Warszawa-Lwów, 1933).Google Scholar
13. Kuratowski, C., Topologie II (Warszawa-Wroclaw, 1950).Google Scholar
14. McCandless, B. H., Retracts and extension spaces for perfectly normal spaces, Michigan J. Math., 9 (1962), 193–197.Google Scholar
15. McCandless, B. H., Retracts and extension spaces for perfectly normal spaces II, Portugal. Math., 22 (1963), 205–207.Google Scholar
16. Michael, E., Some extension theorems for continuous functions, Pacific J. Math., 3 (1953), 789–806.Google Scholar
17. Stone, A. H., Paracompactness and product spaces, Bull. Amer. Math. Soc., 54 (1948), 977–982.Google Scholar
18. Tukey, J. W., Convergence and uniformity in topology, (Princeton, 1940).Google Scholar
19. Wojdyslawski, M., Rétractes absolus et hyperespaces des continus, Fund. Math., 32 (1939), 184–192.Google Scholar