Liminal property
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In mathematics, a phenomenon can be said to occur liminally if, roughly speaking, it occurs on "arbitrarily small" neighborhoods of points. The word locally is traditionally used (ambiguously) for the same purpose, and the term liminally can be used for more clarity when confusion may result.
[edit] Properties of a single space
A topological space can be said to exhibit a property liminally if each point has a neighborhood base of sets exhibiting the property.
[edit] Examples
- Liminally compact and liminally rel-compact topological spaces (locally compact spaces by definitions 3 and 2, respectively),
- Liminally connected and liminally path-connected topological spaces.
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