https://math.codidact.com/categories/41/tags/4645.rssNew Posts Tagged 'connectedness' - MathematicsMathematics - Codidact2023-05-04T13:28:00Zhttps://math.codidact.com/posts/280572Does this generalization of path-connectedness also cover general connectedness?celtschkhttps://math.codidact.com/users/80562021-01-24T14:06:30Z2023-05-04T13:28:00Z<p>I've got the following idea to generalise path-connectedness:</p>
<p>Given a topological space $P$ and a subspace $S$, a space $X$ is $(P,S)$-connected if every continuous function $f:S\to X$ c...https://math.codidact.com/posts/280460What surface do I get by attaching $g$ handles as well as $k$ crosscaps to a sphere?The Amplitwisthttps://math.codidact.com/users/535162021-01-13T18:25:39Z2021-01-13T19:09:42Z<p>I recently found out that there is a classification of compact connected surfaces that says that every such surface (or, $2$-manifold) is homeomorphic to either $S_g$, the sphere with $g \geq 0$...