Abstract
Top spaces with a finite number of identities were studied by several authors. Later right top spaces as a kind of top spaces (with a infinite number of identities) were introduced. In this paper, a wider class of top spaces in which a notion of action is introduced are studied; we call these simple Rees matrices. The set of left invariant vector fields of them are characterized. It is proved that the stabilizer of this action is a subtop space and we give its Lie algebra. It is shown that palais theorem can be generalized for right top spaces. In addition, the quotient space of simple Rees matrices is studied. Finally, it is proved that the restriction of universal covering space of a simple Rees matrix to certain subtop spaces remains a universal covering space.
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