## Presentationsinformation     2006-10-23 (15:15)   •  The seminar room at Vi2

 Talare Erik Melin Titel The joint operator Sammanfattning I would like to introduce the join operator. If $X$ and $Y$ are smallest-neighborhood spaces, i.e., topological spaces where each point has a smallest neighborhood, we can form a new topological space, the join of $X$ and $Y$. Conversely, a space can sometimes be decomposed as a join of simpler spaces. I shall try explain the intuition behind the join operator, and why I have found it useful in my work on digital manifolds. To the best of my knowledge, this operator is not described in the literature. It is my belief that the ideas presented can be used to give simple proofs of the (well-known) facts that (for example) the 8-connected plane and the hexagonal grid are not topological spaces. Hopefully, I will be able to provide such proofs on Monday.