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On Order Paracompact Spaces

Published online by Cambridge University Press:  20 November 2018

Byron H. McCandless
Byron H. McCandless*
Affiliation:
Kent State University, Kent, Ohio
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In (2), Fitzpatrick and Ford defined a class of spaces which they called order totally paracompact. This class of spaces is significant since the order totally paracompact metric spaces constitute the largest known class of spaces for which the small and large inductive dimensions coincide. In this paper we shall consider a class of spaces containing the class of order totally paracompact spaces; we shall call these spaces order paracompact. We shall establish the relationship of this class to the more familiar classes of spaces and obtain an invariance theorem for order paracompact spaces analogous to theorems obtained for various other classes.

In what follows, no separation axioms are assumed unless specifically mentioned. Thus, for example, a Lindelöf space is not taken to be Hausdorff without making the further assumption. Therefore, a Lindelöf space is not necessarily paracompact.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 21 , 1969 , pp. 400 - 405
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Dugundji, J., Topology (Allyn and Bacon, Boston, Massachusetts, 1966).Google Scholar
2. Ben, Fitzpatrick and Ford, R. M., Jr., On the equivalence of small and large inductive dimension in certain metric spaces, Duke Math. J. 34 (1967), 33–38.Google Scholar
3. Gustin, W., Countable connected spaces, Bull. Amer. Math. Soc. 52 (1946), 101–106.Google Scholar
4. Sorgenfrey, R., On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947), 631–633.Google Scholar