Virtual Special Issue - Dedicated to the 120th anniversary of the eminent Russian mathematician P.S. AlexandroffThe complement of a σ-compact subset of a space with a π-tree also has a π-tree

We prove that the complement of a σ-compact subset of a topological space that has a π-tree also has a π-tree. To do this, we construct the foliage hybrid operation, which deals with foliage trees (that is, set-theoretic trees with a 'leaf' at each node). Then using this operation we modify a π-tree of a space and get a π-tree for its subspace.