A hypergraph is a type of graph, \(H=(V,E)\) where V  is the set of nodes and E is the set of hyperedges; where one edge consists of may nodes. Morphological operators are nonlinear operators which can be applied on images, graphs, hypergraphs etc. Dilation and erosion are morphological operators and other operators like opening, closing can be obtained by repeated application of these operators. Topological space consists of a set X together with topology \(\tau \) defined on X, which satisfies the axioms namely Nullset, arbitrary union of opensets and finite intersection of opensets. Such a topological space \(S=(X, T)\) is compatible with a hypergraph H if \(X=V_H \cup E_H\) where \(V_H\) and \(E_H\) are the vertex set and edge set respectively. The morphological operators induces several topology on hypergraph with its compatible topological space \(S=(X, T)\) . Neighborhood of a node is defined in many ways which can be considered as open sets in the corresponding topological space. The purpose of this paper is to apply topological properties on hypergraphs using morphological operators. Separation axiom and closure function are illustrated using hypergraph structure. The work is extended to crime analysis, text processing and patient disease analysis. Topological feature extraction is done on Barcodes created from crime hypergraphs. This gives a better visualization of crime analysis.