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CORR
2011
Springer
162views Education» more  CORR 2011»
12 years 7 months ago
Homology and Robustness of Level and Interlevel Sets
Given a function f : X → R on a topological space, we consider the preimages of intervals and their homology groups and show how to read the ranks of these groups from the exten...
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozo...
DLT
2009
13 years 1 months ago
Closures in Formal Languages and Kuratowski's Theorem
A famous theorem of Kuratowski states that, in a topological space, at most 14 distinct sets can be produced by repeatedly applying the operations of closure and complement to a gi...
Janusz A. Brzozowski, Elyot Grant, Jeffrey Shallit
MLQ
2010
226views more  MLQ 2010»
13 years 2 months ago
The Ultrafilter Closure in ZF
: It is well known that, in a topological space, the open sets can be characterized using filter convergence. In ZF (Zermelo-Fraenkel set theory without the Axiom of Choice), we c...
Gonçalo Gutierres
ORDER
2007
123views more  ORDER 2007»
13 years 3 months ago
2-Dimension from the Topological Viewpoint
In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point ...
Jonathan Ariel Barmak, Elias Gabriel Minian
MLQ
1998
74views more  MLQ 1998»
13 years 3 months ago
Disjoint Unions of Topological Spaces and Choice
We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.
Paul E. Howard, Kyriakos Keremedis, Herman Rubin, ...
MLQ
2002
81views more  MLQ 2002»
13 years 3 months ago
Apartness, Topology, and Uniformity: a Constructive View
The theory of apartness spaces, and their relation to topological spaces (in the point--set case) and uniform spaces (in the set--set case), is sketched. New notions of local decom...
Douglas S. Bridges, Peter Schuster, Luminita V&ici...
JSYML
2002
96views more  JSYML 2002»
13 years 3 months ago
Definitions of Compactness and The Axiom of Choice
We study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.
Omar de la Cruz, Eric J. Hall, Paul E. Howard, Jea...
ENTCS
2007
140views more  ENTCS 2007»
13 years 3 months ago
Admissible Representations of Probability Measures
In a recent paper, probabilistic processes are used to generate Borel probability measures on topological spaces X that are equipped with a representation in the sense of Type-2 T...
Matthias Schröder
ENTCS
2006
106views more  ENTCS 2006»
13 years 3 months ago
Injective Convergence Spaces and Equilogical Spaces via Pretopological Spaces
Sierpinski space is injective in the category Top of topological spaces, but not in any of the larger cartesian closed categories Conv of convergence spaces and Equ of equilogica...
Reinhold Heckmann
CORR
2008
Springer
91views Education» more  CORR 2008»
13 years 3 months ago
Natural pseudo-distance and optimal matching between reduced size functions
We study a dissimilarity measure between shapes, expressed by the natural pseudodistance between size pairs, where a shape is viewed as a topological space endowed with a real-val...
Michele d'Amico, Patrizio Frosini, Claudia Landi