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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Steenrod homology and local connectedness
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by Jerzy Dydak PDF
Proc. Amer. Math. Soc. 98 (1986), 153-157 Request permission

Abstract:

Steenrod homology is used to explain results concerning ${\text {L}}{{\text {C}}^n}$-divisors and one-point compactifications of ${\text {L}}{{\text {C}}^n}$-spaces. It is shown that the one-point compactification $wX$ of a locally compact metrizable space $X$ is ${\text {hl}}{{\text {c}}^n}$ iff $X$ is ${\text {hl}}{{\text {c}}^n}$ and its Steenrod $k$ th homology is finite generated for $k \leqslant n$.
References
  • Glen E. Bredon, Sheaf theory, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0221500
  • A. Borel and J. C. Moore, Homology theory for locally compact spaces, Michigan Math. J. 7 (1960), 137–159. MR 131271
  • Jerzy Dydak, On $\textrm {LC}^{n}$-divisors, Topology Proc. 3 (1978), no. 2, 319–333 (1979). MR 540499
    • —, Local $n$-connectivity of quotient spaces and one-point compactifications, Shape Theory and Geom. Top. Proc. (Dubrovnik, 1981), Lecture Notes in Math., vol. 870, Springer-Verlag, Berlin and New York, 1981, pp. 48-72.
  • Jerzy Dydak, An addendum to the Vietoris-Begle theorem, Topology Appl. 23 (1986), no. 1, 75–86. MR 849095, DOI 10.1016/0166-8641(86)90018-0
  • Jerzy Dydak, Some properties of nearly $1$-movable continua, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 7, 685–689 (English, with Russian summary). MR 464226
  • Jerzy Dydak and Jack Segal, Shape theory, Lecture Notes in Mathematics, vol. 688, Springer, Berlin, 1978. An introduction. MR 520227
  • David A. Edwards and Harold M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics, Vol. 542, Springer-Verlag, Berlin-New York, 1976. MR 0428322
  • Brayton I. Gray, Spaces of the same $n$-type, for all $n$, Topology 5 (1966), 241–243. MR 196743, DOI 10.1016/0040-9383(66)90008-5
    • W. Hurewicz, Homotopie, Homologie, und lokaler Zusammenhang, Fund. Math. 25 (1935), 467-485.
  • Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977
    • K. Kuratowski, Topology, vol. 11, Academic Press, New York, 1968.
  • William S. Massey, Homology and cohomology theory, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 46, Marcel Dekker, Inc., New York-Basel, 1978. An approach based on Alexander-Spanier cochains. MR 0488016
  • J. Milnor, On axiomatic homology theory, Pacific J. Math. 12 (1962), 337–341. MR 159327
    • N. Shrinkhande, Homotopy properties of decomposition spaces, Notices Amer. Math. Soc. 22 (1975). Abstract 757-638.
  • A. Yu. Volovikov and Nguen Le An′, The Vietoris-Begle theorem, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 3 (1984), 70–71 (Russian). MR 749026
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 98 (1986), 153-157
  • MSC: Primary 55N07; Secondary 54F35, 54F43
  • DOI: https://doi.org/10.1090/S0002-9939-1986-0848894-2
  • MathSciNet review: 848894