Call a topology well if and only if every open is compact. The starting point of this note is that this notion generalizes that of well-quasi order, in the sense that an Alexandroff topology is well if and only if its specialisation quasi-ordering is well. For more general topologies, this opens the way to verifying infinite transition systems based on non-well quasi ordered sets, but where the...

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...

Quasi-invariant measures with values in non-Archimedean fields on a group of diffeomorphisms were constructed for non-Archimedean manifolds M in [Lud96, Lud99t]. On non-Archimedean loop groups and semigroups they were provided in [Lud98s, Lud00a, Lud02b]. A Banach space over a local field also serves as the additive group and quasi-invariant measures on it were studied in [Lud03s2, Lud96c]. Thi...

In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that substantially reduces the cos...

In the presence of suitable power spaces, compactness ofX can be characterized as the singleton {∅} being open in the space A(X). Equivalently, this means that universal quantification over a compact space preserves open predicates. Using the language of represented spaces, one can make sense of notions such as a Σ 2 subset of the space of Σ 2 -subsets of a given space. This suggests higher-ord...

In this article, we study the geometry of compact quasi-Einstein manifolds with boundary. We establish sharp boundary estimates for that improve some previous results. Moreover, obtain a characterization theorem such in terms surface gravity components, which leads to new geometric inequality. addition, prove estimate (possibly disconnected) Brown–York mass.

We formulate a new theorem giving several necessary and su‰cient conditions in order that a surjection of the fundamental group p1ðX Þ of a compact Kähler manifold onto the fundamental group Pg of a compact Riemann surface of genus gd 2 be induced by a holomorphic map. For instance, it su‰ces that the kernel be finitely generated. We derive as a corollary a restriction for a group G, fitting in...