Graphical Abstract “My favorite science outreach activity is meeting with young people at fairs to answer the questions they have about world around them (not always easy but often inspiring) … I chose chemistry as a career because you transform and model matter scale of molecule, imperceptible human beings until very recently in our history. …” Find out more Morgan Donnard his Introducing Prof...

I shall start by explaining just what “semi-infinite” means and how it gives rise to interesting structures in geometry. These structures are studied as part of String Theory and are closely related to Floer Theory. Manifolds which carry a “semi-infinite” structure include loop spaces (C∞(S1, M) for M a closed manifold) and the theory seems to have particular simplicities when the original mani...

It is well known that free Boolean algebra on n generators isomorphic to the of functions variables. The distributive lattice monotone In this paper we introduce concept De Morgan function and prove Keywords: Antichain, function, algebra.