For each k = 0, 1, 2, . . . we define an equivalence relation called k-quasi-isotopy on the set of classical links in R3 up to isotopy in the sense of Milnor (1957), such that all sufficiently close approximations of a topological link are k-quasi-isotopic. Whereas 0-quasi-isotopy coincides with link homotopy, 1-quasi-isotopy is not implied by concordance, with aid of the generalized (lk 6= 0) ...

Centreless Lie tori have been used by E. Neher to construct all extended affine Lie algebras (EALAs). In this article, we study isotopy for centreless Lie tori, and show that Neher’s construction provides a 1-1 correspondence between centreless Lie tori up to isotopy and families of EALAs up to isomorphism. Also, centreless Lie tori can be coordinatized by unital algebras that are in general no...

Two distinct isotopy-isomorphy conditions, different from those of J. M. Osborn and Wilson’s condition, for a weak inverse property loop(WIPL) are shown. Only one of them characterizes isotopy-isomorphy in WIPLs while the other is just a sufficient condition for isotopy-isomorphy. Under the sufficient condition called the T condition, Artzy’s result that isotopic cross inverse property loops(CI...