Let $X$ be a topological space and $A$ a subset of $X$. My understanding of a tubular neighborhood $N$ of $A$ is that $N$ is an open set containing $A$ such that $\bar N$ is a manifold with boundary which deformation retracts onto $A$. Is my understanding of tubular neighborhoods correct? and what are the more general conditions we put on $X$ such that a tubular neighborhood exists? i mean by googling i read that when $X$ is a manifold and $A$ is a compact submanifold than such a tubular neighborhood $N$ exists, but what about more general spaces like CW-complexes and so on? Thank you for your help!
Existence of tubular neighborhood
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general-topology
algebraic-topology
manifolds