Abstract For L-power enriched monad ( T , τ ) , the notions of pretopological and topological T -convergence structures are introduced from the viewpoint of topology. It is shown that the pretopological T -convergence structures are exactly the reflexive and unitary ( T , L ) -relations and the topological pretopological T -convergence structures are precisely ( T , L ) -algebras. When ( T , τ ) is the stratified L-filter monad, the L-ordered filter monad, or the L-concave filter monad, the general setting produces known results on stratified L-convergence structures, L-ordered convergence structures and L-concave structures.

中文翻译：

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重新审视一元收敛结构

摘要 对于L-幂富集的单子(T,τ)，从拓扑学的角度引入了前拓扑结构和拓扑T-收敛结构的概念。结果表明，前拓扑T-收敛结构正是自反酉(T,L)-关系，拓扑前T-收敛结构正是(T,L)-代数。当 ( T , τ ) 是分层 L-filter monad、L-ordered filter monad 或 L-concave filter monad 时，一般设置在分层 L-收敛结构、L-ordered 收敛结构和 L-凹结构。