Is box topology in infinite spaces equal to discrete topology always.
2026-03-26 06:05:18.1774505118
Box Topology and Discrete Spaces.
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The only time the box topology on $\displaystyle S = \prod_{i \in I} S_i$ is discrete is when each $S_i$ is discrete. This is revealed by the fact that a given $U \subset S$ is open $\iff \pi_k(U)$ is open for every projection map $\pi_k: S \rightarrow S_k$.