A locally compact T2-space is called a Franklin-Rajagopalan space (or FR-space) provided it has a countable discrete dense subset whose complement is homeomorphic to an ordinal with the order topology. We show that (1) every sequentially compact FR-space X can be identified with a space constructed from a tower T on w (X = X(T)), and (2) for an ultrafilter u on w, a sequentially compact FR-spac...

Viterbo demonstrated that any (2n − 1)-dimensional compact hypersurface M ⊂ (R2n, ω) of contact type has at least one closed characteristic. This result proved the Weinstein conjecture for the standard symplectic space (R2n, ω). Various extensions of this theorem have been obtained since, all for compact hypersurfaces. In this paper we consider non-compact hypersurfaces M ⊂ (R2n, ω) coming from...

Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...

We identify nearby disk galaxies with optical structural parameters similar to those of intermediateredshift compact blue galaxies. By comparing H I and optical emission-line widths, we show that the optical widths substantially underestimate the true kinematic widths of the local galaxies. By analogy, optical emission-line widths may underrepresent the masses of intermediate-z compact objects....

We investigate the quotient algebra $\mathfrak{A}_X^{\mathcal I}:=\mathcal I(X)/\overline{\mathcal F(X)}^{||\cdot||_{\mathcal I}}$ for Banach operator ideals $\mathcal I$ contained in ideal of compact operators, where $X$ is a space that fails I$-approximation property. The main results concern nilpotent algebras $\mathfrak A_X^{\mathcal{QN}_p}$ and A_X^{\mathcal{SK}_p}$ quasi $p$-nuclear opera...

Let δ be a coaction of a locally compact group G on a C*-algebra A. We show that if I is a δ-invariant ideal in A, then 0! I¬δ I G!A¬δ G! (A}I )¬δI G! 0 for full crossed products, as Landstad et al. have done for spatial crossed products by coactions. We prove that for suitable coactions, the crossed products of C ! (X )-algebras are again C ! (X )-algebras, and the crossed products of continuo...

It is shown that almost superdiagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces if the nonlocally convex linear topology τ(p i) is locally bounded. 1. Introduction. The purpose of this paper is to show that almost super-diagonal, polynomially compact operators on the sequence space l(p i) have nontrivial, closed invariant subspaces ...

We show in ZF that: (i) Every subcompact metrizable space is completely metrizable, and every countably subcompact. (ii) A $\mathbf{X}=(X,T)$ compact if only it relative to $T$. (iii) For $\mathbf{X}=(X,T)$, the following are equivalent: \noindent(a) $\mathbf{X}$ compact; \noindent(b) for open filter $\mathcal{F}$ of $\mathbf{X}$, $\bigcap \{\overline{F}\colon F\in \mathcal{F}\}\neq \emptyset $...

Let I ⊂ R be a compact interval symmetric about 0. Let M and N , be compact oriented smooth manifolds of dimensions d and d+1 respectively. We suppose that we have an embedded copy of I ×M inside of N . (See Figure 1). Let N denote the complement of the hypersurface {0} ×M . We consider families ǫ → g(ǫ) of Riemannian metric (tensors) on N each of whose restriction to I ×M is a warped product o...