  The aim of this paper is to study the geometric properties of the point-like
global monopole (briefly, PGM) spacetime, which is a static and spherically
symmetric solution of the Einstein's field equations. It has shown that PGM
spacetime admits various types of pseudosymmetry structures, such as
pseudosymmetry due to Weyl conformal curvature tensor, pseudosymmetry due to
concircular curvature tensor, pseudosymmetry due to conharmonic curvature
tensor, Ricci generalized conformal pseudo-symmetric due to projective
curvature tensor, Ricci generalized projective pseudo-symmetric. Moreover, it
has proved that PGM spacetime is $2$-quasi Einstein, generalized
quasi-Einstein, Einstein manifold of degree $2$, and its Weyl conformal
curvature $2$-forms are recurrent. The energy-momentum tensor of the PGM
spacetime realizes several types of pseudosymmetry, and its Ricci tensor is
compatible with Riemann curvature, Weyl conformal curvature, projective
curvature, and conharmonic curvature and concircular curvature. Further, it has
shown that PGM spacetime admits motion, curvature collineation, and Ricci
collineation. Also, the notion of curvature inheritance (resp., curvature
collineation) for the (1,3)-type curvature tensor is not equivalent to the
notion of curvature inheritance (resp., curvature collineation) for the
(0,4)-type curvature tensor as it has shown that such distinctive properties
were possessed by PGM spacetime. Hence the notions of curvature inheritance
defined by Duggal \cite{Duggal1992} and Shaikh and Datta \cite{ShaikhDatta2022}
are not equivalent.
