inverse function theorem

Summary

inverse function theorem is a theorem^[1]. It ranks in the top 4% of theorem entities by monthly Wikipedia readership (467 views/month).^[2]

Key Facts

• inverse function theorem's image is recorded as Inv-Fun-Thm-3.png^[3].
• inverse function theorem's instance of is recorded as theorem^[4].
• inverse function theorem's part of is recorded as list of theorems^[5].
• inverse function theorem's Freebase ID is recorded as /m/01q5s1^[6].
• inverse function theorem's different from is recorded as implicit function theorem^[7].
• inverse function theorem's defining formula is recorded as \begin{aligned}&f\in\mathcal C^1(M,N)\&\det Df(x)\ne0\implies\exists(x\in U\subset M)\exists(g\colon f(U)\to U)\colon \operatorname{id}U=g\circ f,\;f\circ g=\operatorname{id}{f(U)}\end{aligned}^[8].
• inverse function theorem's MathWorld ID is recorded as InverseFunctionTheorem^[9].
• inverse function theorem's nLab ID is recorded as inverse function theorem^[10].
• inverse function theorem's maintained by WikiProject is recorded as WikiProject Mathematics^[11].
• inverse function theorem's Microsoft Academic ID is recorded as 43987214^[12].
• inverse function theorem's in defining formula is recorded as \det Df^[13].
• inverse function theorem's in defining formula is recorded as \mathcal C^1(-,-)^[14].
• inverse function theorem's in defining formula is recorded as \operatorname{id}^[15].
• inverse function theorem's OpenAlex ID is recorded as C43987214^[16].

Why It Matters

inverse function theorem ranks in the top 4% of theorem entities by monthly Wikipedia readership (467 views/month).^[2] It has Wikipedia articles in 18 language editions, a strong signal of global cultural recognition.^[17] It is known by 11 alternative names across languages and contexts.^[18]