All End Spaces of Infinite Graphs are Paracompact

End spaces of infinite graphs sit at the interface between graph theory, group theory and topology. They arise as the boundary of an infinite graph in a standard sense generalising the theory of the Freudenthal boundary developed by Freudenthal and Hopf in the 1940's. We show that all end spaces of infinite graphs are paracompact. This gives unified and short proofs for a number of results by Diestel, Sprüssel and Polat, and answers an open question about metrizability of end spaces by Polat.

This is joint work with Ruben Melcher and Max Pitz.