We study computability on sequence spaces, as they are used in functional analysis. It is known that non-separable normed spaces cannot be admissibly represented on Turing machines. We prove that under the Axiom of Choice non-separable normed spaces cannot even be admissibly represented with respect to any compatible topology (a compatible topology is one which makes all bounded linear function...

The effect of non-Hermiticity in band topology has sparked many discussions on non-Hermitian topological physics. It long been known that Hamiltonians can exhibit real energy spectra under the condition parity-time ($PT$) symmetry---commonly implemented with balanced loss and gain---but only when is relatively weak. Sufficiently strong non-Hermiticity, other hand, will destroy reality spectra, ...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

In the paradigm of von Neumann and Morgenstern, a representation of a ne preferences in terms of an expected utility can be obtained under the assumption of weak continuity. Since the weak topology is coarse, this requirement is a priori far from being negligible. In this work, we replace the assumption of weak continuity by monotonicity. More precisely, on the space of lotteries on a real open...

In this paper, we prove the existence and multiplicity of solutions for a large class quasilinear problems on nonreflexive Orlicz-Sobolev space. Here, use variational methods developed by Szulkin combined with some properties weak$^*$ topology.

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...

For a compact space $K$ we consider the $P(K)$ of probability regular Borel measures on $K$, equipped with weak$^\ast $ topology inherited from $C(K)^\ast $. We discuss possible characterizations those spaces for which is