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We define and study the notion of \(\mu\)-compact space on Generalized Topological Spaces. A space \((X, \mu)\) is \(\mu\)-compact if every \(\mu\)-open cover of \(X\) has a finite \(\mu\)-open sub cover. We characterize the \(\mu\)-compact space and study their basic properties. The relationship between the \(\mu\)-compact spaces and other well-known spaces are investigated.
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