We introduce the notion of a (strongly) topological lattice $mathcal{L}=(L,wedge ,vee)$ with respect to a subset $Xsubsetneqq L;$ aprototype is the lattice of (two-sided) ideals of a ring $R,$ which is(strongly) topological with respect to the prime spectrum of $R.$ We investigate and characterize (strongly) topological lattices. Given a non-zero left $R$-module $M,$ we introduce and investigate the spectrum $mathrm{Spec}^{mathrm{f}}(M)$ of textit{first submodules} of $M.$ We topologize $mathrm{Spec}^{mathrm{f}}(M)$ and investigate the algebraic properties of $_{R}M$ by passing to the topological properties of the associated space.
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