By Kazimierz Kuratowski

This is often ebook, first released in 1923, republished on 1962, is a cultural and traditionally major paintings, through probably the most very important arithmetic of t he century.

The publication is split into components. the 1st half is dedicated to set idea. It

begins with an account of the algebra of units, together with Boolean algebra, and enormous realization is dedicated to propositional capabilities and quantifiers. [Note: in formula(34) on p. forty four the 1st quantifier at the left might be the common one.]

Additive and multiplicative households of units are brought and likewise Borel households. the ability of aset and cardinal numbers together with the Cantor-Bernstein theorem are mentioned. Ordering kin, well-ordering, ordinal numbers and transfinite induction are absolutely handled. The remedy of those questions is rigorous and complete with no being too designated and whole in each recognize, in order that the publication is appropriate for college students starting a primary severe examine of the subject.

The moment and longer half is dedicated to topology. this can be built from the viewpoint of metric areas, even supposing references are made to non-metric areas at numerous points—for instance while bicompactness is brought, or while the Kuratowski basic closure axioms are given. the normal houses of compact and hooked up areas are received and there are chapters on size, hassle-free homology concept and cuttings of the aircraft, together with the Jordan curve theorem. The author's variety is lucid, and he manages to hide a truly big choice of alternative issues in a relatively brief area.

There are quite a few routines for the coed, of various levels of hassle. The e-book can be invaluable not just as a students' textbook but in addition as a reference book