On conjecture que certains espaces localement étoilés admettent toujours une jolie stratification naturelle, et deviennent ainsi ce qu’on appelle des ensembles. On cite quelques propriétés agréables des ensembles, et quelques exemples exotiques qui distinguent les ensembles, les espaces triangulables, et les espaces localement triangulables.
We show a relation between products of knots, which are generalized from the theory of isolated singularities of complex hypersurfaces, and local moves on knots in all dimensions. We discuss the following problem. Let K be a 1-knot which is obtained from another 1-knot J by a single crossing change (resp. pass-move). For a given knot A, what kind of relation do the products of knots, K ⊗ A and J ⊗ A, have? We characterize these kinds of relation between K ⊗ A and J ⊗ A by using local moves on high...