These include not only various subjects in pure mathematics, but also diverse areas in applied mathematics, including computer science, mathematical physics, economic models, and game theory . Interestingly, one of Spanier's theories, now called Alexander -Spanier homology, is currently being applied to analyse differential equations - a return to Poincaré 's original use of algebraic topology.
Ang mga ito ay hindi lamang sa iba't-ibang mga paksa sa purong matematika, ngunit din magkakaibang lugar na inilapat sa matematika, kasama na ang computer science, matematiko physics, modelo ng ekonomiya, at game theory. Kawili-wili, isa sa Spanier's theories, ngayon tinatawag Alexander-Spanier homology, ay kasalukuyang inilalapat sa Analyze kaugalian equation - isang bumalik sa Poincaré 's orihinal na gumamit ng algebraic topology.