Abstract
Some properties of property Q are stated, some new results are proved and implications to totally metacompact and totally paracompact are obtained.
Highlights
An open cover has property Q [1] ifwhen {Oi E N} is a sequence ofdistinct members of the cover and p, qi are points of Oi and {Pi} has lhnit p, {q} has lirnit p
A topological space is metacompact if each open cover has a point tinite refinement that covers the space
Some previous results pertaining to property Q are: THEOREM 1
Summary
An open cover has property Q [1] ifwhen {Oi E N} is a sequence ofdistinct members of the cover and p, qi are points of Oi and {Pi} has lhnit p, {q} has lirnit p. A topological space is metacompact if each open cover has a point tinite refinement that covers the space. Topological space is totally paracompact (totally metacompact) if each open base contains a locally finite (point finite) subcover. [2] A space that satisfies property Q is metacompact.
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