Feebly compact space
From Topospaces
This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces
This is a variation of compactness. View other variations of compactness
Contents
Definition
A topological space is termed feebly compact or lightly compact if every locally finite collection of nonempty open subsets is finite.
Relation with other properties
Stronger properties
| property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
|---|---|---|---|---|
| Compact space | Every open cover has a finite subcover | compact implies feebly compact | feebly compact not implies compact | |FULL LIST, MORE INFO |
Weaker properties
| property | quick description | proof of implication | proof of strictness (reverse implication failure) | intermediate notions |
|---|---|---|---|---|
| Pseudocompact space | Image of continuous map to reals is bounded | feebly compact implies pseudocompact | pseudocompact not implies feebly compact | |FULL LIST, MORE INFO |
