This book serves as an introduction to an area of computability theory that originated in the
1950s, and since then has fanned out in many different directions under the influence of …

We combine homotopy type theory with axiomatic cohesion, expressing the latter internally
with a version of 'adjoint logic'in which the discretization and codiscretization modalities are …

Represented spaces form the general setting for the study of computability derived from
Turing machines. As such, they are the basic entities for endeavors such as computable …

We investigate the topological aspects of some algebraic computation models, in particular
the BSS-model. Our results can be seen as bounds on how different BSS-computability and …

An old and celebrated analogy says that writing programs is like proving theorems. This
analogy has been productive in both directions, but in particular has demonstrated …

We study the computational difficulty of the problem of finding fixed points of nonexpansive
mappings in uniformly convex Banach spaces. We show that the fixed point sets of …

Computability theory, which investigates computable functions and computable sets, lies at
the foundation of computer science. Its classical presentations usually involve a fair amount …

Banach's contraction mapping principle is remarkable in its simplicity, yet it is perhaps the
most widely applied fixed point theorem in all of analysis with special applications to the …

Recent work of several authors shows that many categories of interest to topologists can be
represented as categories of lax algebras. In this paper we introduce the concept of a …

We introduce and study the notion of overt choice for countably-based spaces and for
CoPolish spaces. Overt choice is the task of producing a point in a closed set specified by …