This article initiates the study of topological transcendental fields F which are subfields field C all complex numbers such that only consists rational and a nonempty set numbers. F, with topology it inherits as subspace C, is field. Each separable metrizable zero-dimensional space algebraically Q(T), extension by T It proven there exist precisely 2?0 countably infinite each homeomorphic to Q ...

We consider the isometry group of infinite dimensional separable hyperbolic space with its Polish topology. This topology is given by pointwise convergence. For non-locally compact groups, some striking phenomena like automatic continuity or extreme amenability may happen. Our leading idea to compare this topological usual Lie groups on one side and non-Archimedean $\mathcal{S}_\infty$, all per...

We continue from “part I” our address of the following situation. For a Tychonoff space Y, the “second epi-topology” σ is a certain topology on C(Y), which has arisen from the theory of categorical epimorphisms in a category of lattice-ordered groups. The topology σ is always Hausdorff, and σ interacts with the point-wise addition + on C(Y) as: inversion is a homeomorphism and + is separately c...

Let F denote C or Q` for a prime ` 6= char(k), equipped with its natural topology, and let Gk = Gal(ks/k) for a choice of separable closure ks/k. For each place v of k choose a separable closure kv,s/kv and an embedding ks ↪→ kv,s over k ↪→ kv, thereby identifying Gkv with a decomposition group at v in Gk. It is surprising (but confirmed by consultation with experts) that the following natural ...

In this paper we establish a direct connection between stable approximate unitary equivalence for ∗-homomorphisms and the topology of the KK-groups which avoids entirely C*-algebra extension theory and does not require nuclearity assumptions. To this purpose we show that a topology on the Kasparov groups can be defined in terms of approximate unitary equivalence for Cuntz pairs and that this to...

In this paper, we present a simple axiomatization of useful topologies, i.e., topologies on an arbitrary set, with respect to which every continuous total preorder admits utility representation. We introduce the concept weak open and closed countable chain condition (WOCCC) relative topology, then show that topology always satisfies condition. The most important result in paper shows completely...

The goal of this paper is to give an approach to constructing transfer homomorphisms along such maps π for abelian sheaves and presheaves of spectra which holds generally for the standard geometric topologies on the category Sch|S of schemes of finite type over S, satisfies the usual properties, and specializes to known phenomena. The construction displayed here, called the separable transfer, ...

This paper generalizes polyhedra to infinite dimensional separable Hilbert spaces as countable intersections of closed semispaces. We show that a polyhedron is the sum of convex proper subset, which is compact in the product topology, plus a closed pointed cone plus a closed subspace. In the final part the dual range space technique is extended to solve infinite dimensional LP problems.

We show that every abelian Polish group is the topological factor-group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.

In this paper we study the role of cleavability and divisibility in the topology of generalized ordered (GO-)spaces. We characterize cleavability of a GOspace over the class of metrizable spaces, and over the spaces of irrational and rational numbers. We present a series of examples related to characterizations of cleavability over separable metric spaces and over the space of real numbers.