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...
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...
It is well -known that a topology for a space can be described in
terms of neighborhood systems, closed sets, closure operator or convergence
as well as open sets. In fact, it is also possible to describe
a topology in terms of interior operator or boundary operator. This
paper is...
This paper defines and discusses some of the separation
axioms of topological spaces. In the cases considered,
a search is made for sets of conditions which
would be equivalent in a space satisfying a given separation
axiom to the existence of a family of real valued,
continuous functions which separates...
This paper defines four function space topologies,
characterizes two of them in terms of more familiar
concepts, and compares the four topologies. Then in the
cases of the two less familiar topologies we have considered
several common properties of topological spaces
and attempted to answer the following question: If the...
In this thesis a relatively new topological technique, due to A. Granas, called Topological Transversality is used to obtain existence theorems for initial and boundary value problems in a variety of settings. This fixed point result is based on the notions of an essential map and on a priori bounds...
In this paper we consider the behavior of certain surfaces at
certain boundary points. The surfaces under consideration satisfy
a topological definition and are of 2-dimension in 3-dimensional
Euclidean space with the boundary a finite set of straight line
segments. It is shown that the surface of minimum area with...
In this thesis some applications of algebraic topology
are given. Kirchhoff's circuit laws are translated into the
language of algebraic topology: If G is the graph of
a network N, if i is a current distribution and if v is
a voltage distribution of N, then the two Kirchhoff laws...
