Related papers: A Rado theorem for complex spaces
We extend Deuber's theorem on $(m,p,c)$-sets to hold over the multidimensional positive integer lattices. This leads to a multidimensional Rado theorem where we are guaranteed monochromatic multidimensional points in all finite colorings of…
We give a short proof for the Hartogs's extension theorem on (n-1)-complete complex spaces.
We extend Carleson's formula to radially polynomially weighted Dirichlet spaces.
We discuss Nakamaye's Theorem and its recent extension to compact complex manifolds, together with some applications.
Semistable reduction theorem for projective morphisms in the category of complex analytic spaces is established.
We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.
We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.
We shall prove an extension of the semipositivity theorem for the case of reducible algebraic fiber spaces.
We prove a general extension theorem for holomorphic line bundles on reduced complex spaces, equipped with singular hermitian metrics, whose curvature currents can be extended as positive, closed currents. The result has applications to…
Some generalizations of the classical Hurewicz formula are obtained for extension dimension and C-spaces.
We extend the original Cachazo-Douglas-Seiberg-Witten conjecture for symmetric spaces.
The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for…
We prove that every manifold of dimension $\ge 2$ admitting a conformal structure is paracompact.
We fully characterise the solvability of Rado equations inside linear combinations $a_{1}\U\oplus\dots\oplus a_{n}\U$ of idempotent ultrafilters $\U\in\beta\Z$ by exploiting known relations between such combinations and strings of integers.…
We generalise the Caristi Fixed Point Theorem to the mappings of the complete semi-metric spaces.
We investigate under what conditions holomorphic forms defined on the regular locus of a reduced complex space extend to holomorphic (or logarithmic) forms on a resolution of singularities. We give a simple necessary and sufficient…
We extend Hadamard's Lemma to the setting of a separable Hilbert space.
We present a generalization of the Radon-Riesz property to sequences of continuous functions with values in uniformly convex and uniformly smooth Banach spaces.
We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.
We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle,…