Related papers: Some results related to the continuity problem

Let $E,F$ be two topological spaces and $u:E\rightarrow F$ be a map. \ If $F$ is Haudorff and $u$ is continuous, then its graph is closed. \ \ The Closed Graph Theorem establishes the converse when $E$ and $F$ are suitable objects of…

We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions…

The classical result of Landau on the existence of kings in finite tournaments (=finite directed complete graphs) is extended to continuous tournaments for which the set X of players is a compact Hausdorff space. The following partial…

Let $\A$ be the operator which assigns to each $m \times n$ matrix-valued function on the unit circle with entries in $H^\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \times n$ matrix-valued functions…

In a well generated triangulated category T, given a regular cardinal a, we consider the following problems: given a functor from the category of a-compact objects to abelian groups that preserves products of <a objects and takes exact…

The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.

We are studying long term sequence prediction (forecasting). We approach this by investigating criteria for choosing a compact useful state representation. The state is supposed to summarize useful information from the history. We want a…

Absolute continuity implies uniform continuity, but generally not vice versa. In this short note, we present one sufficient condition for a uniformly continuous function to be absolutely continuous, which is the following theorem: For a…

The paper deals with a class of cooperative functional differential equations (FDEs) with infinite delay, for which sufficient conditions for persistence and permanence are established. Here, the persistence refers to all solutions with…

In this paper we study the existence and uniqueness of fixed points of a class of mappings defined on complete, (sequentially compact) cone metric spaces, without continuity conditions and depending on another function.

For topological spaces $X$ and $Y$, a (not necessarily continuous) function $f:X \rightarrow Y$ naturally induces a functor from the category of closed subsets of $X$ (with morphisms given by inclusions) to the category of closed subsets of…

The exponential map that characterises the flows of vector fields is the key in understanding the basic structural attributes of control systems in geometric control theory. However, this map does not exists due to the lack of completeness…

We examine the analogues for the respective categories of locales of two well-known results about regularity and effectiveness of some categories of spaces. We show that the category of compact regular locales is effective regular…

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features,…

Orderability, weak orderability and the existence of continuous weak selections on filter spaces (i.e., spaces with a single non-isolated point) and their products are discussed. We prove that a closed continuous image X of a suborderable…

A combination of deep reinforcement learning and supervised learning is proposed for the problem of active sequential hypothesis testing in completely unknown environments. We make no assumptions about the prior probability, the action and…

We prove an existence result for the principal-agent problem with adverse selection under general assumptions on preferences and allocation spaces. Instead of assuming that the allocation space is finite-dimensional or compact, we consider…

The main result of this paper is a proof of the continuity of a family of integral functionals defined on the space of functions of bounded variation with respect to a topology under which smooth functions are dense. These functionals occur…

For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…

We define and study obvious strategy-proofness with respect to a partition of the set of agents. It encompasses strategy-proofness as a special case when the partition is the coarsest one and obvious strategy-proofness when the partition is…