# Manifold with no closed components?

Let $$M$$ be a manifold with boundary. Reading some papers on $$3$$-manifolds I have come across some statements where they require that: ”$$M$$ has no closed components.”

What does this mean? The obvious interpretation is that no connected components are closed, but connected components are always closed, so this is not the correct statement.

• A closed manifold is a compact manifold with empty boundary. Thus, it is not refering to the definition of closed sets of a topological space. See en.m.wikipedia.org/wiki/Closed_manifold – Panagiotis Konstantis Feb 2 at 10:55
• @PanagiotisKonstantis So if I understand you correctly, the ”no closed components” simply mean that we are working with a manifold where every connected component either is open, or has boundary? – Dedalus Feb 2 at 11:25
• That's correct. – Najib Idrissi Feb 2 at 11:29