We obtain an embedding theorem for compact strongly pseudoconvex CR manifolds which are bounadries of some complete Hermitian manifolds. We use this to compactify some negatively curved Kähler manifolds with compact strongly pseudoconvex boundary. An embedding theorem for Sasakian manifolds is also derived.

Obviously each lattice that satisfies either (JID) or (MID) is distributive. A classic result in lattice theory is Funayama’s theorem [5] stating that there is an embedding e of L into a complete Boolean algebra B that preserves all existing joins and meets in L iff L satisfies both (JID) and (MID). Funayama’s original proof was quite involved. For complete L, Grätzer [6, Sec. II.4] gave a more...

We show how the Gaussian min-max theorem provides direct proofs of several famous results in asymptotic geometric analysis, such as, the Dvoretzky theorem, the Johnson-Lindenstrauss Lemma, Gluskin’s theorem on embedding in `1 , and others.

We demonstrate under appropriate finiteness conditions that a coarse embedding induces an inequality of homological Dehn functions. Applications the main results include characterization what finitely presentable groups may admit into hyperbolic group geometric dimension 2, characterizations subgroups with quadratic function and to embeddings nilpotent other same growth groups.

The Dushnik–Miller Theorem states that every infinite countable linear ordering has a nontrivial self-embedding. We examine computability-theoretical aspects of this classical theorem.

The structure of a sofic shift space is investigated, and Krieger’s embedding theorem and Boyle’s factor theorem are generalized to a large class of sofic shifts.