in this paper we introduce the concept of topological number for locally convex topological spaces and prove some of its properties. it gives some criterions to study locally convex topological spaces in a discrete approach.

Abstract We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and ‘tensor symmetry’. a general of lattice Hamiltonians which allow certain level nonlocality. Based on assumption dual we explicitly construct low energy excited states. also derive ’t Hooft anomaly for after ‘gauging’ symmetries. A 3d system anomalous 1-form can...

in this paper we find sufficient conditions on primitive inverse topological semigroup s under which: the inversion inv : (h(s)) (h(s)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed h-classes is topologically isomorphic to an orthogonal sum p i2= bi (gi) of topological brandt extensions bi (gi) of countably compac...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or transition can emerge in many-body system. We derive topological partition functions that characterize LSM spin systems with $G_s\times G_{int}$ symmetry, where $G_s$ is an arbitrary space group one two spatial dimensions, and $G_{int}$ any internal symmetry whose project...

In this paper, we define topological hyperrings and study their basic concepts which supported by illustrative examples. We show some differences between topological rings and topological hyperrings. Also, by the fundamental relation $\Gamma^{*}$, we indicate the role of complete parts (saturated subsets) and complete hyperrings in topological hyperrings and specially we show that if every (clo...