On absolutely universal embeddings

On absolutely universal embeddings

It is well known that, given a point-line geometry Γ and a projective embedding ε : Γ → PG(V ), if dim(V ) equals the size of a generating set of Γ, then ε is not derived from any other embedding. Thus, if Γ admits an absolutely universal embedding, then ε is absolutely universal. In this paper, without assuming the existence of any absolutely universal embedding, we give sufficient conditions ...

Towards Universal Paraphrastic Sentence Embeddings

We consider the problem of learning general-purpose, paraphrastic sentence embeddings based on supervision from the Paraphrase Database (Ganitkevitch et al., 2013). We compare six compositional architectures, evaluating them on annotated textual similarity datasets drawn both from the same distribution as the training data and from a wide range of other domains. We find that the most complex ar...

Isometric Embeddings and Universal Spaces

We show that if a separable Banach space Z contains isometric copies of every strictly convex separable Banach space, then Z actually contains an isometric copy of every separable Banach space. We prove that if Y is any separable Banach space of dimension at least 2, then the collection of separable Banach spaces which contain an isometric copy of Y is analytic non Borel.

On Absolutely Continuous Transformations

On Absolutely Divergent Series

We show that in the א2-stage countable support iteration of Mathias forcing over a model of CH the complete Boolean algebra generated by absolutely divergent series under eventual dominance is not isomorphic to the completion of P (ω)/fin. This complements Vojtáš’ result, that under cf(c) = p the two algebras are isomorphic [15].