Related papers: Unbounded towers and the Michael line topology

It is proved that any countable topological vector space over a finite field $\mathbb F_p$ or, equivalently, any countable Abelian topological group of prime exponent has a closed discrete basis.

For a new class of topological vector spaces, namely $\kappa $-normed spaces, and associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a $\kappa…

The tubular geometry (T-geometry) is a generalization of the proper Euclidean geometry, founded on the property of sigma-immanence. The proper Euclidean geometry can be described completely in terms of the world function $\sigma =\rho…

In this paper we provide new characterizations of the Gehring-Hayman theorem from the point of view of Gromov boundary and uniformity. We also determine the critical exponents for the uniformized space to be a uniform space in the case of…

We prove a conjecture of Toponogov on complete convex planes, namely that such planes must contain an umbilic point, albeit at infinity. Our proof is indirect. It uses Fredholm regularity of an associated Riemann-Hilbert boundary value…

We characterize which cobounded quasigeodesics in the Teichmueller space T of a closed surface are at bounded distance from a geodesic. More generally, given a cobounded lipschitz path gamma in T, we show that gamma is a quasigeodesic with…

A group topology is said to be linear if open subgroups form a base of neighborhoods of the identity element. It is proved that the existence of a nondiscrete extremally disconnected group of Ulam nonmeasurable cardinality with linear…

Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…

A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X, closed under finite intersections.…

Given a complex number $c$, define the divisor function $\sigma_c:\mathbb N\to\mathbb C$ by $\sigma_c(n)=\sum_{d\mid n}d^c$. In this paper, we look at $\overline{\sigma_{-r}(\mathbb N)}$, the topological closures of the image of…

In a Euclidean path integral formulation of gauge theory and quantum mechanics, the theta-term induces a sign problem, and relatedly, a complex phase for the fugacity of topological defects; whereas in Minkowskian formulation, it induces a…

A discrete subset $S$ of a topological group $G$ is called a {\it suitable set} for $G$ if $S\cup \{e\}$ is closed in $G$ and the subgroup generated by $S$ is dense in $G$, where $e$ is the identity element of $G$. In this paper, the…

Given a regular cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$, we study a class of toposes with enough points, the $\kappa$-separable toposes. These are equivalent to sheaf toposes over a site with $\kappa$-small limits that has at…

Let $G$ be a simple algebraic group over an algebraically closed field $k$ and let $C_1, \ldots, C_t$ be non-central conjugacy classes in $G$. In this paper, we consider the problem of determining whether there exist $g_i \in C_i$ such that…

The abelian sigma model in (1+1) dimensions is a field theoretical model which has a field $ \phi : S^1 \to S^1 $. An algebra of the quantum field is defined respecting the topological aspect of the model. It is shown that the zero-mode has…

We prove an equivariant version of the classical Menger-Nobeling theorem regarding topological embeddings: Whenever a group $G$ acts on a finite-dimensional compact metric space $X$, a generic continuous equivariant function from $X$ into…

Genus $g$ Torelli space is the moduli space of genus $g$ curves of compact type equipped with a homology framing. The hyperelliptic locus is a closed analytic subvariety consisting of finitely many mutually isomorphic components. We use…

Topological insulators are a new class of materials which have gapped spectra in the bulk, but are accompanied by topologically protected gapless excitations at the surface (edge) of the system. These phenomena have a close relationship…

We study here the topology of information on the space of probability measures over Polish spaces that was defined in Hellwig (1996). We show that under this topology, a convergent sequence of probability measures satisfying a conditional…

In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…