The Cantor set is a compact, totally disconnected, perfect
subset of the real line. In this paper it is shown that two non-empty,
compact, totally disconnected, perfect metric spaces are homeomorphic.
Furthermore, a subset of the real line is homeomorphic
to the Cantor set if and only if it is...
Row equivalence, equivalence, and similarity of matrices are studied; some problems concerning an extension of these relations to infinite matrices are discussed.
In the study of uniform convergence, one is led naturally to
the question of how uniform convergence on subsets relates to uniform convergence on the whole space. This paper develops theorems on how pointwise convergence relates to uniform convergence
on finite sets, how uniform convergence on finite subsets relates to...
This work contains a brief history of the four color problem
from 1840 to 1890. This includes Kempe's attempted proof of the
problem as well as maps which illustrate Heawood's discussion of
Kempe's error. The remaining part is a discussion of Kempe's and
Story's work on patching out maps. Story...
Proving mathematical theorems usually involves the proof of
an implication, p --> q. Often it is convenient to prove the implication
by proving one which is equivalent to or "stronger" than the original
theorem. Proofs of this type are called indirect proofs.
In Chapter I five forms of indirect proofs...