Izotopy

Izotopy is a term used in several fields to denote related ideas of sameness or deformation. The two most common senses are in chemistry, where it refers to isotopes of the same element, and in topology, where isotopy describes a continuous deformation between objects.

In chemistry, isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons, yielding different mass numbers. They share nearly identical chemical behavior but differ in nuclear properties such as stability and decay modes. Some isotopes are stable (for example, carbon-12 and carbon-13), while others are radioactive (carbon-14). Isotopes are studied to determine ages of rocks and fossils, trace chemical and biological processes, and are used in medical imaging and therapy. Natural abundance of isotopes varies by element and context.

In topology and geometry, isotopy is a concept describing a continuous deformation between objects. A family of maps f_t from a space M into another space N, with t in [0,1], is an isotopy if f_0 equals one map and f_1 equals another, and each f_t preserves the relevant structure. When the ambient space itself is deformed by a family of homeomorphisms H_t of N, sending one subspace to another, the two subspaces are ambient isotopic. In knot theory, two knots are isotopic if such an ambient isotopy exists, making isotopy a central tool in distinguishing knot types from plain homotopy.

Outside topology, isotopy also appears in algebra as the notion of an isotope of an algebra or a loop, obtained by modifying the multiplication with fixed invertible maps. This yields related algebraic structures used in the study of nonassociative algebras.

The term derives from Greek iso, equal, and topos, place.