Snake-like space

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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| \le 1.