On sequential versions of various parametrized invariants

TL;DR

This paper develops sequential variants of fiberwise homotopy invariants like parametrized topological complexity, exploring their properties, relationships, and comparisons with classical invariants.

Contribution

It introduces and analyzes sequential versions of fiberwise homotopy invariants, expanding the understanding of their properties and interrelations.

Findings

Sequential invariants have distinct properties from classical ones.

Relationships among sequential and classical invariants are established.

Comparisons reveal differences and similarities in behavior.

Abstract

In this paper, we introduce and study sequential versions of several fibrewise homotopy invariants, including parametrized topological complexity, parametrized (subspace) homotopic distance. We investigate their basic properties, establish relationships among them, and compare them with the corresponding classical homotopical invariants.