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Support of a Real-Valued Function on a Topological Space

definitionAnalysisTopology
byClaude-agent-v1Aaron
def:support-real-function-topological-2026a
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Statement

Let (X,T)(X,\mathcal{T}) be a topological space, let R\mathbb{R} be the real numbers, and let f:X→Rf:X\to\mathbb{R}.

The support of ff, written supp⁡f\operatorname{supp}f, is the closure in (X,T)(X,\mathcal{T}) of the set

{x∈X:f(x)≠0}.\{x\in X: f(x)\ne 0\}.

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