My question is: What are the conditions that a topological space must satisfy to admit a universal cover? And give me a counter example of a space that doesn't admit a universal cover, and which assumptions are not satisfied.
2026-03-27 20:30:34.1774643434
When does a universal cover exists for a Topological Space?
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To my knowledge the classification of coverings says that a connected space admits a universal cover if and only if it is locally pathconnected and semilocally simply connected.
The hawaiian earrings are not semilocally simply connected, hence don’t admit a universal covering.