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Assuming countable choice, the lower-limit line is normal
Statement
Assuming the Axiom of Countable Choice, the lower-limit line is normal.
Facts & Assumptions
Given: The Axiom of Countable Choice.
Under countable choice, the lower-limit line is regular and Lindelöf (The lower-limit line has a clopen basis, is regular, and is Lindelöf under countable choice).
Every regular Lindelöf space is normal (Every regular Lindelöf space is normal).
Proof
Under the stated hypothesis, [L1] supplies a regular Lindelöf lower-limit line.
Applying [L2] gives its normality.
Depends on
Used by
Dependency tree · two levels
9 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- L. A. Steen and J. A. Seebach, Counterexamples in Topology, Sorgenfrey line (standard reference, not scraped)
- Sorgenfrey topology (Encyclopedia of Mathematics) (standard reference, not scraped)