Let $\tilde{X}$ be a two-sheeted cover of a connected topological space X. If $\tilde{X}$ is disconnected then this has exactly two components. Further each component is homeomorphic to X by the covering projection. Can anyone give the argument for this statement ?
2026-05-04 12:24:21.1777897461
Two sheeted disconnected cover of a connected topological space has exactly two components
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