Theorem T000676

Has a point with a unique neighborhood ∧ Locally injectively path connected ⇒ Injectively path connected

$X$ has a point $p$ whose only neighborhood is $X$. As $X$ is Locally injectively path connected, $p$ has a Injectively path connected neighborhood. Hence, $X$ is Injectively path connected.

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• Converse
• References

The converse ( Injectively path connected ⇒ Has a point with a unique neighborhood ∧ Locally injectively path connected ) cannot be proven from other theorems or disproven from a counterexample.

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