https://yukar.icu/tags/manifold/Recent content in Manifold on Yukari's BlogHugozh-cnWed, 03 Jun 2026 00:00:00 +0000https://yukar.icu/posts/manifold/1/Wed, 03 Jun 2026 00:00:00 +0000https://yukar.icu/posts/manifold/1/<p>Reference: Introduction to Smooth Manifolds by John M. Lee.</p> <hr> <p>A topological space $M$ is a <strong>topological manifold</strong> of dimension $n$ if $M$ is locally Euclidean of dimension $n$, where <strong>locally Euclidean</strong> means that for every point $p \in M$, there exists an open neighborhood $U$ of $p$ in $M$ and a homeomorphism $\varphi: U \to B^n$, then we obtain a set of such <strong>charts</strong> $\{(U_\alpha, \varphi_\alpha)\}$ called a <strong>topological atlas</strong> on $M$.</p>