Topological ubiquity of trees

Let ⊲ be a relation between graphs. We say graph G is -ubiquitous if whenever Γ with n for all ∈ N , then one also has ℵ 0 where αG the disjoint union of α many copies . The Ubiquity Conjecture Andreae, well-known open problem in theory infinite graphs, asserts that every locally finite connected ubiquitous respect to minor relation. In this paper we show trees are topological relation, irrespective their cardinality. This answers question Andreae from 1979.