Izreki o kompaktnosti

Predstavimo izrek N. Feldmana in J. Dydaka, ki vsaki zaprti unitalni podalgebri zveznih omejenih funkcij na topološkem prostoru priredi kompakten Hausdorffov prostor, ki zadošča določenim lastnostim glede na dano podalgebro. Kot posledice izpeljemo nekaj znanih izrekov splošne topologije: Stone-Weierstrassov izrek, Stone-Čechovo kompaktifikacijo, Tietzejev razširitveni izrek in izrek Tihonova.

Theorems on compactness

We prove a theorem of N. Feldman and J. Dydak, which associates to every closed unital subalgebra of bounded functions on a topological space a compact Hausdorff space satisfying certain properties with regards to the subalgebra in question. We derive as corollaries a number of well-known point-set topology results, namely the Stone-Weierstrass theorem, Stone-Čech compactification, Tietze extention theorem, and Tychonoff theorem.