proposition: Corollary f_inv_homeomorphism : homeomorphism f_inv.
proof: Proof. apply compact_hausdorff_homeo. - apply quotient_compact. apply R_closed_interval_compact. lra. - apply Hausdorff_Subspace. apply Hausdorff_ProductTopology2. all: apply metrizable_Hausdorff. all: apply RTop_metrizable. - apply f_inv_bijective. - apply f_inv_continuous. Qed.
imports: Coq(Reals.Ratan Lia Lra Logic.IndefiniteDescription Program.Subset) ZornsLemma(Quotients) Topology(ProductTopology AdjunctionSpace SubspaceTopology RTopology RFuncContinuity Homeomorphisms)