Existence of Metacompact Space which is not Paracompact
Jump to navigation
Jump to search
Theorem
There exists at least one example of a metacompact topological space which is not also a paracompact space.
Proof
Let $T$ be the Dieudonné plank.
From Dieudonné Plank is Metacompact, $T$ is a metacompact space.
From Dieudonné Plank is not Paracompact, $T$ is not a paracompact space.
Hence the result.
$\blacksquare$
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $3$: Compactness: Paracompactness