CORR
2011
Springer
13 years 3 months ago
2011
Springer
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...
DLT
2009
13 years 9 months ago
2009
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...
MLQ
2010
13 years 10 months ago
2010
: 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...
ORDER
2007
13 years 11 months ago
2007
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 ...
MLQ
1998
13 years 11 months ago
1998
We find properties of topological spaces which are not shared by disjoint unions in the absence of some form of the Axiom of Choice.
MLQ
2002
13 years 11 months ago
2002
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...
JSYML
2002
13 years 11 months ago
2002
We study the relationships between definitions of compactness in topological spaces and the roll the axiom of choice plays in these relationships.
ENTCS
2007
13 years 11 months ago
2007
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...
ENTCS
2006
13 years 12 months ago
2006
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...
CORR
2008
Springer
13 years 12 months ago
2008
Springer
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...