The following theorem is proved. THEOREM. Let X be a homogeneous continuum such that Hl(X) ^ 0. Ij'$/ is the collection of maximal terminal proper subcontinua of X, then (1) The collection ff is a monotone, continuous, terminal decomposition ofX, (2) The nondegenerate elements of%? are mutually homeomorphic, indecomposable, cell-like, terminal, homogeneous continua of the same dimension as X, (...

We consider countable Borel equivalence relations on quotient Borel spaces. We prove a generalization of the representation theorem of Feldman–Moore, but provide some examples showing that other very simple properties of countable equivalence relations on standard Borel spaces may fail in the context of nonsmooth quotients. In this paper we try to analyze some very basic questions about the str...

If a Lie group acts on a manifold freely and properly, pulling back by the quotient map gives an isomorphism between the differential forms on the quotient manifold and the basic differential forms upstairs. We show that this result remains true for actions that are not necessarily free nor proper, as long as the identity component acts properly, where on the quotient space we take differential...

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space G/H if H is non-compact. The first half of the article elucidates general machinery to study discontinuous groups for G/H, followed by the most update and complete l...

The theory of moduli of morphisms on P generalizes the study of rational maps on P1. This paper proves three results about the space of morphisms on P of degree d > 1, and its quotient by the conjugation action of PGL(n + 1). First, we prove that this quotient is geometric, and compute the stable and semistable completions of the space of morphisms. This strengthens previous results of Silverma...

The problem of constructing moduli space of vector bundles over a projective manifold has attracted many mathematicians for decades. In mid 60’s Mumford first constructed the moduli space of vector bundles over algebraic curves via his celebrated GIT machinery. Later, in early 80’s Atiyah and Bott found an infinite dimensional symplectic quotient description of this moduli space. Since then, we...

Abstract A complex screen is an arrangement of panels that may not be even locally orientable because junction lines. comprehensive trace space framework for first-kind variational boundary integral equations on screens has been established in Claeys and Hiptmair (Integr Equ Oper Theory 77:167–197, 2013. https://doi.org/10.1007/s00020-013-2085-x ) the Helmholtz equation, 84:33–68, 2016. https:/...

The aim of this paper is to develop an individual neural network generation and ensemble algorithm based on quotient space granularity clustering. Firstly, we give the characteristics of the quotient space granularity and affinity propagation(AP) clustering. Secondly, we introduce the quotient space concept to the AP clustering analysis, which can find an optimal granularity from all possible g...

This article discusses the existence problem of a compact quotient of a symmetric space by a properly discontinuous group with emphasis on the non-Riemannian case. Discontinuous groups are not always abundant in a homogeneous space G/H if H is non-compact. The first half of the article elucidates general machinery to study discontinuous groups for G/H , followed by the most update and complete ...