Is my proof that the product of covering spaces is a covering space …
2015年8月22日 · Let $p_1:\tilde X_1 \rightarrow X_1$ and $p_2:\tilde X_2 \rightarrow X_2$ be two covering spaces. Prove: $p = p_1 \times p_2:\tilde X_1 \times \tilde X_2 \rightarrow X_1 \times X_2$ is a covering space.
Product of coverings is a covering of product space.
$U_1$ and $U_2$ both hold these properties, because $p_i$ is a covering space. Hence $U_1=\bigcup_{l\in L}$ and $U_2=\bigcup_{j\in J}$ are both disjoint unions of open sets. Then $U=\bigcup_{(l,j)\in L\times J} U_l\times U_j$
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In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto itself. In particular, coverings are special types of local homeomorphisms .
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