AbstractLet G be an n-dimensional geometric lattice with a topology. Assume that each level set Gj of j-flats is open. As compatibility conditions we postulate the continuity of joining with points and of meeting with hyperplanes. Assuming further a “stability” axiom, a theory of these “Topological n-spaces” is developed. This is offered as a solution to Birkhoff's Problem 88
One may topologise an incidence structure by imposing that the operations of joining points and inte...
A closure space (J,−) is called a convex geometry (see, for example, [1]), if it satisfies the anti-...
Given a set X , let P(X) be the collection of all subsets of X . A nonempty sub-collection u, of P(X...
AbstractLet G be an n-dimensional geometric lattice with a topology. Assume that each level set Gj o...
AbstractIt is shown that for n ⩾ 3, essentially every nondiscrete topological n-space is strongly em...
We consider the geometric join of a family of subsets of the Euclidean space. This is a construction...
A geometric join is the union of all colorful simplices spanned by a colored point set in the d-dime...
AbstractA geometry structure on a category is defined in analogy with the structure of geometric lat...
In this paper a solution of Whitehead’s problem is presented: Starting with a purely mereological sy...
AbstractWe present some results on combinatorial geometries (geometric lattices) in which closure is...
International audienceA lattice L is spatial if every element of L is a join of completely join-irre...
AbstractEvery arrangement H of affine hyperplanes in Rd determines a partition of Rd into open topol...
The purpose of this paper is to give several different characterizations of those T0-spaces E with t...
This chapter discusses the bouquets of geometric lattices. Matroid theory is in the center of Combin...
AbstractThe purpose of this paper is to give several different characterizations of those T0-spaces ...
One may topologise an incidence structure by imposing that the operations of joining points and inte...
A closure space (J,−) is called a convex geometry (see, for example, [1]), if it satisfies the anti-...
Given a set X , let P(X) be the collection of all subsets of X . A nonempty sub-collection u, of P(X...
AbstractLet G be an n-dimensional geometric lattice with a topology. Assume that each level set Gj o...
AbstractIt is shown that for n ⩾ 3, essentially every nondiscrete topological n-space is strongly em...
We consider the geometric join of a family of subsets of the Euclidean space. This is a construction...
A geometric join is the union of all colorful simplices spanned by a colored point set in the d-dime...
AbstractA geometry structure on a category is defined in analogy with the structure of geometric lat...
In this paper a solution of Whitehead’s problem is presented: Starting with a purely mereological sy...
AbstractWe present some results on combinatorial geometries (geometric lattices) in which closure is...
International audienceA lattice L is spatial if every element of L is a join of completely join-irre...
AbstractEvery arrangement H of affine hyperplanes in Rd determines a partition of Rd into open topol...
The purpose of this paper is to give several different characterizations of those T0-spaces E with t...
This chapter discusses the bouquets of geometric lattices. Matroid theory is in the center of Combin...
AbstractThe purpose of this paper is to give several different characterizations of those T0-spaces ...
One may topologise an incidence structure by imposing that the operations of joining points and inte...
A closure space (J,−) is called a convex geometry (see, for example, [1]), if it satisfies the anti-...
Given a set X , let P(X) be the collection of all subsets of X . A nonempty sub-collection u, of P(X...
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