Add to ORKGGraduation date: 1965The Cantor set is a compact, totally disconnected, perfect\ud subset of the real line. In this paper it is shown that two non-empty,\ud compact, totally disconnected, perfect metric spaces are homeomorphic.\ud Furthermore, a subset of the real line is homeomorphic\ud to the Cantor set if and only if it is obtained from a closed interval\ud by removing a class of disjoint, separated from each other but\ud sufficiently dense open intervals
The Cantor Set is a famous topological set developed from an infinite process of starting with the i...
AbstractThe following result, and a closely related one, is proved: If u:X → Y is an open, perfect s...
In [3] Knaster and Reichbach proved that any homeo morphism defined on a closed subset P of the Cant...
Copyright © 2013 Edgar A. Cohen. This is an open access article distributed under the Creative Commo...
A Cantor Space is any topological space that is homeomorphic to the Cantor Set. Cantor Spaces are pr...
It is a famous result of Alexandroff and Urysohn [1] that every compact metric space is a continuous...
Abstract. It is shown that the hyperspace of nonempty (bounded) closed subsets CldH(X) (BddH(X)) of ...
The purpose of this paper is to explore some of the properties of the Cantor set and to extend the i...
Abstract. A metric space (X, d) is monotone if there is a linear order < on X and a constant c su...
Definition A Cantor set is a compact, completely disconnected set without isolated points Theorem An...
We study the subsets of metric spaces that are negligible for the infimal length of connecting curve...
AbstractLet C ⊂ R be a compact totally disconnected subset of the real line R and [0, 1] ⊂ R, the cl...
We prove under Martin’s Axiom that every separable metrizable space represented as the union of less...
ABSTRACT. We show that a compact O-dimensional subset X of Rn(n •> 2) can be moved off itself ins...
We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is hom...
The Cantor Set is a famous topological set developed from an infinite process of starting with the i...
AbstractThe following result, and a closely related one, is proved: If u:X → Y is an open, perfect s...
In [3] Knaster and Reichbach proved that any homeo morphism defined on a closed subset P of the Cant...
Copyright © 2013 Edgar A. Cohen. This is an open access article distributed under the Creative Commo...
A Cantor Space is any topological space that is homeomorphic to the Cantor Set. Cantor Spaces are pr...
It is a famous result of Alexandroff and Urysohn [1] that every compact metric space is a continuous...
Abstract. It is shown that the hyperspace of nonempty (bounded) closed subsets CldH(X) (BddH(X)) of ...
The purpose of this paper is to explore some of the properties of the Cantor set and to extend the i...
Abstract. A metric space (X, d) is monotone if there is a linear order < on X and a constant c su...
Definition A Cantor set is a compact, completely disconnected set without isolated points Theorem An...
We study the subsets of metric spaces that are negligible for the infimal length of connecting curve...
AbstractLet C ⊂ R be a compact totally disconnected subset of the real line R and [0, 1] ⊂ R, the cl...
We prove under Martin’s Axiom that every separable metrizable space represented as the union of less...
ABSTRACT. We show that a compact O-dimensional subset X of Rn(n •> 2) can be moved off itself ins...
We show that the space of all Lelek fans in a Cantor fan, equipped with the Hausdorff metric, is hom...
The Cantor Set is a famous topological set developed from an infinite process of starting with the i...
AbstractThe following result, and a closely related one, is proved: If u:X → Y is an open, perfect s...
In [3] Knaster and Reichbach proved that any homeo morphism defined on a closed subset P of the Cant...