Snake-like space

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

Definition

A topological space is termed snake-like if it is a compact Hausdorff space where every open cover has an finite open refinement $\{U_{0},U_{1},\ldots U_{n}\}$ such that $U_{i}\cap U_{j}$ is nonempty for $|i-j|\leq 1$.