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In this paper, we introduce the Itô-Henstock integral of an operator-valued stochastic process and formulate a version of Itô's formula.

In this paper, we formulate a version of Itô's formula for the backwards Itô-Henstock integral of an operator-valued stochastic process. Itô's formula is the stochastic analogue of the change of variable for deterministic integrals.

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In this study, the concept of θ s -open set is introduced. The topology formed by θ s -open sets is strictly finer than the topology formed by θ-open sets but is not comparable with the topology formed by ω θ -open sets. Related concepts such as θ sopen and θ s -closed functions, θ s -continuous function, θ s -connected space, and some versions of separation axioms are defined and characterized. Finally, the concept of θ s -continuous function from an arbitrary topological space into the product space is investigated further.