3 results
Uniform Paracompactness and Uniform Para-Lindelöfness
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- Journal:
- Canadian Mathematical Bulletin / Volume 29 / Issue 4 / 01 December 1986
- Published online by Cambridge University Press:
- 20 November 2018, pp. 392-397
- Print publication:
- 01 December 1986
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Even Covering Properties and Somewhat Normal Spaces
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- Journal:
- Canadian Mathematical Bulletin / Volume 29 / Issue 2 / 01 June 1986
- Published online by Cambridge University Press:
- 20 November 2018, pp. 154-159
- Print publication:
- 01 June 1986
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A topological space X is said to be somewhat normal provided that for each open cover
is a normal cover of X. We show that a completely regular somewhat normal space need not be normal, thereby answering a question of W. M. Fleischman. We note that a collectionwise normal somewhat normal space need not be almost 2-fully normal, as had previously been asserted, and that neither the perfect image nor the perfect preimage of a somewhat normal space has to be somewhat normal.
is a normal cover of The Shrinking Property
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- Journal:
- Canadian Mathematical Bulletin / Volume 26 / Issue 4 / 01 December 1983
- Published online by Cambridge University Press:
- 20 November 2018, pp. 385-388
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- 01 December 1983
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A space has the shrinking property if, for every open cover {Va | a ∈ A}, there is an open cover {Wa | a ∈ A} with
for each a ∈ A.lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property.
for each a ∈ A.lt is strangely difficult to find an example of a normal space without the shrinking property. It is proved here that any ∑-product of metric spaces has the shrinking property.