Related papers: An open day in the metric space

These informal notes were prepared in connection with a lecture at a high school mathematics tournament, and provide an overview of some examples of metric spaces and a few of their basic properties.

Metric spaces are a fundamental component of mathematics and have a paramount importance as a framework for measuring distance. They can be found in many different branches of mathematics, such as analysis and topology. This paper offers an…

The formal definition of limit is one mathematical idea that gives difficulties to most students. Therefore, it is necessary to provide engaging activity in order to construct the students' understanding about the definition. This study…

This short survey has been prepared in connection with the workshop on discrete metric spaces and their applications at Princeton, August, 2003, and tries to convey some of the ways that one might look at functions on metric spaces in…

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

This is a pedagogical introduction covering maps of metric spaces, Gromov-Hausdorff distance and its "physical" meaning, and dilation structures as a convenient simplification of an exhaustive database of maps of a metric space into…

In this article, we introduce the concept of lexicographic metric space and, after discussing some basic properties of these metric spaces, such as completeness, boundedness, compactness and separability, we obtain a formula for the metric…

The aim of the present article is to give an introduction to the concept of quasi-unitary equivalence and to define several (pseudo-)metrics on the space of self-adjoint operators acting possibly in different Hilbert spaces. As some of the…

In spacetime physics, we frequently need to consider a set of all spaces (`universes') as a whole. In particular, the concept of `closeness' between spaces is essential. However, there has been no established mathematical theory so far…

The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.

The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

We created an introductory physics activity for undergrad students consisting in measuring by different methods the same physical quantity. It allows to confront students with questions of uncertainty, precision, and model versus theory.…

As subjects perceive the sensory world, different stimuli elicit a number of neural representations. Here, a subjective distance between stimuli is defined, measuring the degree of similarity between the underlying representations. As an…

Artificial intelligence (AI) is everywhere, with many children having increased exposure to AI technologies in daily life. We aimed to understand middle school girls' (a group often excluded group in tech) perceptions and knowledge gaps…

This is a write-up of a talk given at the CATMI meeting in Bergen in July 2023, and is an introduction to a category-theoretic perspective on metric spaces. A metric space is a set of points such that between each pair of points there is a…

Students in inquiry science classrooms face an essential tension between sharing new ideas and critically evaluating those ideas. Both sides of this tension pose affective risks that can discourage further discussion, such as the…

In this paper, the authors propose a software metric called Class Activeness Metric which helps to determine the level of accessibility of the members of a class when it is instantiated as objects. Object interactions need to be straight…

In this article we present the prototype of a workshop on naive set theory designed for high school students in or around the seventh year of primary education. Our concept is based on two events which the author organized in 2006 and 2010…

Similarity search is an important problem in information retrieval. This similarity is based on a distance. Symbolic representation of time series has attracted many researchers recently, since it reduces the dimensionality of these high…