Finite topological spaces<br>Notes and reading materials on finite topological spaces
Notes written for the REU, and slides of a survey talk
Finite topological spaces<br>(pdf)<br>Low dimensional examples<br>(pdf)<br>Finite spaces and simplicial complexes<br>(pdf)<br>An introduction to simplicial sets (JULY 21)<br>(pdf)<br>A few exercises and problems about finite topological spaces<br>(UPDATED July 6)<br>(pdf)<br>Finite groups and finite spaces<br>(pdf)<br>Subdivisions of small categories<br>(pdf)<br>An outline summary of basic point set topology<br>(pdf)<br>Slides of a talk on finite topological spaces<br>(pdf)
Selected papers and a thesis about finite topological spaces
A. Fix and S. Patrias. Enumeration of homotopy classes of finite T_0<br>topological spaces. [REU paper]<br>(pdf)<br>J. Salvatore. The weak homotopy equivalence of S^n and a space with<br>2n+2 points. [REU paper]<br>(pdf)<br>E. Clader. Inverse limits of finite topological spaces [Undergraduate paper]<br>(pdf)<br>M. Kukiela. On homotopy types of Alexandroff spaces [Undergraduate paper]<br>(pdf)<br>J.A. Barmak (PhD thesis). Algebraic toplogy of finite topological spaces and applications<br>(pdf)<br>J.A. Barmak and E.G. Minian. Minimal finite models<br>(pdf)<br>T. Osaki. Reduction of finite topological spaces<br>(pdf)<br>J.A. Barmak and E.G. Minian. Simple homotopy types and finite spaces<br>(pdf)<br>J.A. Barmak and E.G. Minian. One-point reductions of finite spaces, h-regular<br>CW-complexes and collapsibility<br>(pdf)<br>J.A. Barmak and E.G. Minian. Strong homotopy types, nerves, and collapses<br>(pdf)<br>J.A. Barmak and E.G. Minian. 2-Dimension from the topological viewpoint [combinatorics]<br>(pdf)<br>J.A. Barmak and E.G. Minian. Automorphism groups of finite posets [group theory]<br>(pdf)<br>J.A. Barmack. On Quillen's theorem A for posets [homotopy theory of posets]<br>(pdf)<br>K.A. Hardie, J.J.C. Vermeulen, and P.J. Witbooi. A nontrivial pairing of<br>finite $T_0$-spaces<br>(pdf)<br>K.A. Hardie and P.J. Witbooi. Crown multiplications and a higher order<br>Hopf construction<br>(pdf)<br>K.A. Hardie, S. Salbany, J.J.C. Vermeulen, and P.J. Witbooi.<br>(pdf)<br>J. Cupal, S. Kopp, P.F. Stadler. RNA shape space topology [biology!]<br>(pdf)<br>Rina Foygel. 2nd subdivision of a simplicial set (or category)<br>(pdf)