Local connectedness in transformation groups

Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces

We apply Preuss' concept of $mbbe$-connectedness to the categories of lattice-valued uniform convergence spaces and of lattice-valued uniform spaces. A space is uniformly $mbbe$-connected if the only uniformly continuous mappings from the space to a space in the class $mbbe$ are the constant mappings. We develop the basic theory for $mbbe$-connected sets, including the product theorem. Furtherm...

Remarks on Punctual Local Connectedness

We study the condition, on a connected and locally connected geometric morphism p : E → S, that the canonical natural transformation p∗ → p! should be (pointwise) epimorphic — a condition which F.W. Lawvere [11] called the ‘Nullstellensatz’, but which we prefer to call ‘punctual local connectedness’. We show that this condition implies that p! preserves finite products, and that, for bounded mo...

Connectedness of Degree Graphs of Nonsolvable Groups

On Formal Local Cohomology and Connectedness

Let a denote an ideal of a local ring (R, m). Let M be a finitely generated Rmodule. There is a systematic study of the formal cohomology modules lim ←− H m(M/a M), i ∈ Z. We analyze their R-module structure, the upper and lower vanishing and non-vanishing in terms of intrinsic data of M, and its functorial behavior. These cohomology modules occur in relation to the formal completion of the pun...

On local gamma factors for orthogonal groups and unitary groups

‎In this paper‎, ‎we find a relation between the proportionality factors which arise from the functional equations of two families of local Rankin-Selberg convolutions for‎ ‎irreducible admissible representations of orthogonal groups‎, ‎or unitary groups‎. ‎One family is that of local integrals of the doubling method‎, ‎and the other family is‎ ‎that of local integrals expressed in terms of sph...