Constructive uniformities of pseudometrics and Bishop topologies

Quotient topologies in constructive set theory and type theory

The standard construction of quotient spaces in topology uses full separation and power sets. We show how to make this construction using only the (generalised) predicative methods available in constructive type theory and constructive set theory. MSC: primary 03F65, 54B15, secondary 03B15, 03E70.

Minimal structures , generalized topologies , and ascending systems should not be studied without generalized uniformities

By using the Pervin relations, we show that all minimal structures, generalized topologies, and ascending systems can be naturally derived from generalized uniformities. Therefore, they need not be studied separately.

Clusters, Concepts, and Pseudometrics

The fields of cluster analysis and concept analysis are both used to identify patterns in data. Concept analysis identifies similarities between sets of objects based on their attributes. Cluster analysis groups objects with related characteristics based on some notion of distance. In this paper, we investigate connections between these two approaches. In particular, for each binary relation de...

Homo restis - constructive control through modular string topologies

In this paper we discuss a modular instrument system for musical expression consisting of multiple devices using string detection, sound synthesis and wireless communication. The design of the system allows for different physical arrangements, which we define as topologies. In particular we will explain our concept and requirements, the system architecture including custom magnetic string senso...

Contextual Uniformities