Given topological manifolds $M,N$ of the same dimension, let $\operatorname{Emb}(M,N)$ denote the subspace of $\operatorname{Map}(M,N)$ consisting of the (topological) embeddings $M\to N$. Here $\operatorname{Map}(M,N)$ is equipped with the compact-open topology.
It is stated in Notation 5.4.1.9 of Jacob Lurie's Higher Algebra that, if $M$ is a topological manifold of dimension $k$, the map $$\operatorname{Emb}(\mathbb{R}^k,M)\to M$$ induced by the evaluation at $0\in\mathbb{R}^k$ is a Serre fibration.
This probably has to do with some variation of the isotopy extension theorem. Unfortunately I am not conversant with manifold topology. Does anyone know a refernce (or a proof, if it is short enough to fit into this page) for this claim? Thanks in advance.