相关论文: A few remarks concerning complex-analytic metric s…

A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.

We consider a subanalytic subset A of a complex analytic manifold M (when M is viewed as a real manifold) and formulate conditions under which A is a complex analytic subset of M.

A few aspects of self-similarity related to complementary components of closed subsets of R^n are briefly discussed.

We give a proof of the fact tha the subset of the rational curves form a closed analytic subset in the space of the 1-dimensional cycles of a complex space.

The first section of this modest survey reviews some basic notions and describes some families of examples, and the second section briefly indicates some general aspects of analysis on metric spaces. The remaining three sections are…

There is proved the sufficiency of several conditions for the removability of singularities of complex-analytic sets in domains of $\mathbb C^n$.

This paper is concerned with analysis on metric spaces in a variety of settings and with several kinds of structure.

We present examples of realcompact spaces with closed subsets that are C*-embedded but not C-embedded, including one where the closed set is a copy of the space of natural numbers.

The main purpose of this paper is to study complex valued metric-like spaces as an extension of metric-like spaces, complex valued partial metric spaces, partial metric spaces, complex valued metric spaces and metric spaces. In this…

On R^n endowed with a riemannian metric of bounded nonpositive curvature, the weakly convex closed subsets are topologically trivial. The stability of such subsets under intersection characterizes the euclidean spaces.

We build an elementary analytico-geometric theory of Segre chains and their jets.

This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.

We explore representing the compact subsets of a given represented space by infinite sequences over Plotkin's $\mathbb{T}$. We show that computably compact computable metric spaces admit representations of their compact subsets in such a…

We investigate algebraic and analytic subvarieties of C^n with automorphisms which can not be extended to the ambient space.

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we study strict subsets, i.e. sets whose variational capacity with respect to a larger reference set is finite, in the case $p=1$.…

An open (resp., closed) subset A of a topological space (X, T ) is called C-open (resp., C-closed) set if cl(A) \ A (resp., A \ int(A)) is a countable set. This paper aims to present the concept of C-open and C-closed sets. We first…

This is a slightly revised version of lectures notes for a course in Summer 2022 joint between Bonn and Copenhagen, intended as a stable citable version. The goal of this course is to make our general approach to analytic geometry via…

We show that the set of points of an overt closed subspace of a metric completion of a Bishop-locally compact metric space is located. Consequently, if the subspace is, moreover, compact, then its collection of points is Bishop compact.

The work consists of solutions of metric problems for convex and finite subsets of geodesic spaces.