Is is known that a Banach space contains an isomorphic copy of $c_0$ if, and only it can be equivalently renormed to almost square. We introduce study transfinite versions square spaces with the purpose relating them

When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid lines: linear, transfinite and weighted. Linear method does not preserve the known values along the g...

In a general setting, the transfinite interpolation problem requires constructing a single function´Üµ that takes on the prescribed values and/or derivatives on some collection of point sets. The sets of points may contain isolated points, bounded or unbounded curves, as well as surfaces and regions of arbitrary topology. All such closed semi-analytic sets may be represented implicitly by real ...

We show that the space of transfinite words, is, ordinal-indexed over a Noetherian is also Noetherian, under natural topology which we call regular subword topology. characterize its sobrification and specialization ordering

Abstract We study the existence of transformations transfinite plane that allow one to reduce Ramsey-theoretic statements concerning uncountable Abelian groups into classical partition relations for cardinals. To exemplify: we prove every inaccessible cardinal $\kappa $ , if admits a stationary set does not reflect at inaccessibles, then negative relation \nrightarrow [\kappa ]^2_\kappa implies...