In this paper we introduce and study so-called k∗-metrizable spaces forming a new class of generalized metric spaces, and display various applications of such spaces in topological algebra, functional analysis, and measure theory. By definition, a Hausdorff topological space X is k∗-metrizable if X is the image of a metrizable space M under a continuous map f : M → X having a section s : X → M ...

Non-archimedean seminorms on rings and modules provide in general a structure which is richer than the associated linear topology [3], [2]. We want to characterize Banach spaces and commutative algebras over a complete non-trivially valued nonarchimedean field K, as linearly topologized modules over the ring of integers K◦ of K, with no reference to any specific norm. This is analog to the clas...

The aim of this paper is to give the dimension of the space of Siegel modular forms M k (Γ(3)) of degree 2, level 3 and weight k for each k. Our main result is Theorem dim M k (Γ(3)) = 1 2 (6k 3 − 27k 2 + 79k − 78) k ≥ 4. In other words we have the generating function : ∞ k=0 dim M k (Γ(3))t k = 1 + t + t 2 + 6t 3 + 6t 4 + t 5 + t 6 + t 7 (1 − t) 4. About the space of cusp forms, the dimension ...

Gauge-invariant strings in the 3d U(1)+Higgs theory K. Kajantie, M. Laine, T. Neuhaus, J. Peisa, A. Rajantie, K. Rummukainen Theory Division, CERN, CH-1211 Geneva 23, Switzerland Helsinki Institute of Physics, P.O.Box 9, 00014 University of Helsinki, Finland Department of Physics, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K. NORDITA, Blegdamsvej 17, DK-2100 Copenhagen Ø, D...

The statistical properties of spectra quantum systems within the framework random matrix theory is widely used in many areas physics. These are affected, if two or more sets superposed, resulting from discrete symmetries present system. Superposition $m$ such circular orthogonal, unitary and symplectic ensembles studied numerically using higher-order spacing ratios. For given Dyson index $\beta...

Let F be a local field and n ≥ 2 an integer. We study the Radon transform as an operator M : C+ → C− from the space of smooth K-finite functions on Fn \ {0} with bounded support to the space of smooth K-finite functions on Fn \{0} supported away from a neighborhood of 0. These spaces naturally arise in the theory of automorphic forms. We prove that M is an isomorphism and provide formulas for M...

2.1 Dimension and codimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Dimension relative to a base . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4 Cartier divisors . . . . . . . . . . . . . . . . . . . . . . . . . . . ...