Vipul: Created page with "==Definition== The '''Vietoris topology''' is a topology defined on the set of all non-empty subsets of a topological space based on the topology on the original topo..."

2012-12-21T00:01:42Z

Created page with "==Definition== The '''Vietoris topology''' is a topology defined on the set of all non-empty subsets of a topological space based on the topology on the original topo..."

New page

==Definition==

The '''Vietoris topology''' is a [[topology]] defined on the set of all non-empty subsets of a [[topological space]] based on the topology on the original topological space. The topology is defined by the following [[basis]]:

{{quotation|For every non-empty finite collection of non-empty open subsets <math>U_1,U_2,\dots, U_n</math> in <math>X</math>, the corresponding basis element is the set of all non-empty subsets <math>A</math> of <math>X</math> for which ''all'' the intersections <math>A \cap U_i</math> are non-empty.}}

Vietoris topology - Revision history

Vipul: Created page with "==Definition== The '''Vietoris topology''' is a topology defined on the set of all non-empty subsets of a topological space based on the topology on the original topo..."