Title: When lots of LOTS make a LOTS (joint work with Dave Lutzer).  

Abstract:  A LOTS is a topological space which admits a linear ordering such that the topology of the space is generated by the basis of open intervals.   The union of two LOTS need not be a LOTS (consider, e.g., the closed interval [0,1] and the open interval (2,3)).   However, we shall prove that if the spaces are locally compact and 0-dimensional, then the topological sum of any number (finite or infinite) of LOTS is again a LOTS.