OAL 16 : Conference in Honor of the 90 th Birthday of Bernhard Banaschewski

In the last talk of this conference, Joanne Walters-Wayland will discuss a continuum of minimizable properties of sublocales of a (completely regular) locale. By that is meant a property P such that above any dense sublocale S of a locale L there is a least sublocale having property P. Such properties induce a contraction of the lattice of prenuclei of the frame, i.e., an order-preserving map which moves each prenucleus down (≤), and has certain other properties. In fact the minimizable properties are in bijective correspondence with the prenuclear contractions. The idea is that the contractions give us a handle on the corresponding minimal dense sublocales, particularly if we have formulas for them. In effect, this amounts to a recursive technique for defining sublocales with certain minimality properties. More important, the formulas themselves suggest new minimizable properties. This talk will be a gentle introduction to these ideas, with a few examples sprinkled in. Time of talk: Friday, June 10, 2016 10:45 11:25 Filters in Algebraic Frames Papiya Bhattacharjee Penn State Behrend e-mail: [email protected] Abstract In this talk, we will discuss convergence of various classical filters of an algebraic frame. Also, we will compare filters of the frame versus filters of the base of compact elements. This is a joint work with Inderasan Naidoo.In this talk, we will discuss convergence of various classical filters of an algebraic frame. Also, we will compare filters of the frame versus filters of the base of compact elements. This is a joint work with Inderasan Naidoo. Time of talk: Friday, June 10, 2016 12:15 12:35