On Covering Maps

General Topology
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Tsakanikas Nickos
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On Covering Maps

#1

Post by Tsakanikas Nickos »

Let \( X \) and \( Y \) be topological spaces and let \( p \ \colon X \longrightarrow Y \) be a continuous map.
  1. If \( p \) is a covering map, then show that \( p \) is a local homeomorphism.
  2. Show that the converse of \( (1) \) is not true.
  3. Show that if \( p \) is a proper local homeomorphism, then \( p \) is a covering map.
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