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A simple and efficient method for the synthesis of pyrazolopyranopyrimidines under solvent-free has been developed. The one-pot multicomponent condensation of arylaldehydes with hydrazine hydrate, ethyl acetoacetate and barbituric acid in the vicinity of a mesoporous basic nanomagnetic catalyst, namely DBU immobilized on Fe3O4@nSiO2@mSiO2 was synthesized in remarkably high yields and in short reaction times. Significantly, this catalyst can be easily separated from the reaction media by applying an external magnet, and can be reused for several cycles.

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2.
Cut-point spaces     
The notion of a cut-point space is introduced as a connected topological space without any non-cut point. It is shown that a cut-point space is infinite. The non-cut point existence theorem is proved for general (not necessarily ) topological spaces to show that a cut-point space is non-compact. Also, the class of irreducible cut-point spaces is studied and it is shown that this class (up to homeomorphism) has exactly one member: the Khalimsky line.

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