Ever seen the little ‘You Are Here’ dot on a map of the airport, or the mall, or any other structure? That’s a demonstration of the Brouwer Fixed-Point Theorem. Violently shaken martini shakers and ...

This is a preview. Log in through your library . Abstract We prove constructively that, in order to derive the uniform continuity theorem for pointwise continuous mappings from a compact metric space ...

I'm trying to understand the Gaussian process sample continuity theorem stated on page 35. The text says: The following result is adequate for most settings arising in practice and may be proven as a ...

Abstract: Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a ...

Abstract: Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a ...

Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

We present old and new results about the size function of a set providing simple and complete proofs using basic tools of general topology. For instance, the decomposition of the size function is ...