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Group topologies coarser than the Isbell topology

机译：组拓扑比Isbell拓扑更粗糙

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摘要

The Isbell, compact-open and point-open topologies on the set C(X,M) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α(X) of compact families of open subsets of a topological space X. Those α(X) for which addition is jointly continuous at the zero function in C_α(X,K) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α(X) for which C_α(X,R) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, that C_α(X, R) can be strictly finer than the compact-open topology, are given. To our knowledge, this is the first example of a splitting group topology strictly finer than the compact-open topology.
机译：连续实值映射的集合C（X，M）上的Isbell，紧凑开放和点开放拓扑可以表示为关于a的开放子集的紧凑族的某些集合α（X）的对偶拓扑表征了在C_α（X，K）的零函数处加法共同连续的那些α（X），并找到了使翻译连续的充分条件。结果，规范地定义了C_α（X，R）为拓扑向量空间的集合α（X）。当且仅当X为次同音时，Isbell拓扑与此向量空间拓扑一致。给出了基于测度理论方法的示例，其中C_α（X，R）可以比紧凑开放拓扑更严格。据我们所知，这是严格比紧凑开放式拓扑更好的拆分组拓扑的第一个示例。

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