In this paper by definition of generalized action of generalized Lie groups (top spaces) on a manifold, the concept of stabilizer of the top spaces is introduced. We show that the stabilizer is a top space, moreover we find the tangent space of a stabilizer. By using of the quotient spaces, the dimension of some top spaces are fined.

We define and characterize the harmonic Besov space Bp, 1 ≤ p ≤ ∞, on the unit ball B in Rn. We prove that the Besov spaces Bp, 1 ≤ p ≤ ∞, are natural quotient spaces of certain Lp spaces. The dual of Bp, 1 ≤ p < ∞, can be identified with Bq , 1/p + 1/q = 1, and the dual of the little harmonic Bloch space B0 is B1.

We prove that if X is an analytic adic space with an action of a finite group G, a categorical adic space quotient X/G exists under a mild hypothesis, in analogy with a classical result for schemes. We also show that if X is perfectoid, then X/G is perfectoid in many cases.

This paper takes a new look at some old spaces. The old spaces are the moduli spaces of complete collineations, introduced and explored by many of the leading lights of 19th-century algebraic geometry, such as Chasles, Schubert, Hirst, and Giambelli. They are roughly compactifications of the spaces of linear maps of a fixed rank between two fixed vector spaces, in which the boundary added is a ...

The absolute change in the Rayleigh quotient (RQ) is bounded in this paper in terms of the norm of the residual and the change in the vector. If x is an eigenvector of a self-adjoint bounded operator A in a Hilbert space, then the RQ of the vector x, denoted by (x), is an exact eigenvalue of A. In this case, the absolute change of the RQ j(x) (y)j becomes the absolute error for an eigenvalue (x...

The paper studies the class of analytic input/state/output systems for which the vector fields and the observation functions are only partially defined. The state space of the system is a universe space a newly defined concept. As an example, quotient systems and observability are studied in detail. Observability is defined in a new way, consistent with the “universal” approach.

We prove that every separable metric space which admits an `1tree as a Lipschitz quotient, has a σ-porous subset which contains every Lipschitz curve up to a set of 1-dimensional Hausdorff measure zero. This applies to any Banach space containing `1. We also obtain an infinite-dimensional counterexample to the Fubini theorem for the σ-ideal of σ-porous sets.

We prove formal GAGA for good moduli space morphisms under an assumption of “enough vector bundles” (which holds for instance for quotient stacks). This supports the philosophy that though they are non-separated, good moduli space morphisms largely behave like proper morphisms.

The local intersection cohomology of a point in the Baily–Borel compactification (of a Hermitian locally symmetric space) is shown to be canonically isomorphic to the weighted cohomology of a certain linear locally symmetric space (an arithmetic quotient of the associated self-adjoint homogeneous cone). Explicit computations are given for the symplectic group in four variables. Mathematics Subj...

In this paper we improve some mapping theorems on א-spaces. For instance we show that an א-space is preserved by a closed and countably bi-quotient map. This is an improvement of Yun Ziqiu’s theorem: an א-space is preserved by a closed and open map.