In this paper, we study the difference spaces F(Δ)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {F}}(\varDelta )$$\end{document}, F0(Δ)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {F}}_0(\varDelta )$$\end{document}, [F](Δ)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {[F]}}(\varDelta )$$\end{document} and [F]0(Δ)\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {[F]}}_0(\varDelta )$$\end{document} of double sequences obtained as the domain of four-dimensional backward difference matrix Δ\documentclass[12pt]{minimal}
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\begin{document}$$\varDelta $$\end{document} in the spaces F\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {F}}$$\end{document}, F0\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {F}}_{0}$$\end{document}, [F]\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {[F]}}$$\end{document} and [F]0\documentclass[12pt]{minimal}
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\begin{document}$${\mathcal {[F]}}_{0}$$\end{document} of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.
