Using the concept of H-open set, we introduce the concept of H-compact space. Several properties of H-compact spaces are proved , among these are:H-closed subset of H-compact is     H-compact.The continuoues image of H-compact     is H-compact.H-compact subset of H-Hausdorff is     H-closed.
In this work, neutral stochastic functional differential equations with infinite delay (NSFDEwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space C r under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L 2 and exponential estimates of NSFDEwID have been studied.
In this work, neutral stochastic functional differential equations with infinite delay (NSFD-EwID) have been addressed. By using the Euler-Maruyama scheme and a localization argument, the existence and uniqueness of solutions to NSFDEwID at the state space Cr under the local weak monotone condition, the weak coercivity condition and the global condition on the neutral term have been investigated. In addition, the L2 and exponential estimates of NSFDEwID have been studied.
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