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Hereditarily locally compact separable spaces

Part of the Lecture Notes in Mathematics book series (LNM,volume 719)

Abstract

We first obtain some neat characterizations of hereditarily locally compact separable spaces. The first section includes also some characterizations of minimal one among them. The second section describes intrinsically the one-point-compactifications of such spaces. It is also proved that a compact Hausdorff sequential space of type (2,1) fails to be Frechet if and only if it contains one such space as a subspace. Thus a good class of test spaces for Frechet property is obtained here in answer to a problem of Arhangelskii and Franklin. In constrast no this we like to mention that it was proved in [R1] that S2 cannot be a test space for sequential spaces of order 2.

Key words

  • Sequential space
  • type (2,1)
  • test space
  • Ψ*
  • A.M.S. classification (1970)
  • 5452
  • 5440
  • 5422

This author had an NSF contract MCS 77-22201 when this paper was written.

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References

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© 1979 Springer-Verlag

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Kannan, V., Rajagopalan, M. (1979). Hereditarily locally compact separable spaces. In: Herrlich, H., Preuß, G. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065271

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  • DOI: https://doi.org/10.1007/BFb0065271

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09503-3

  • Online ISBN: 978-3-540-35193-1

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