闭包空间中的真拓扑与容许拓扑
Proper and admissible topologies in the setting of closure spaces
摘要：
一个Cech闭包空间$(X,u)$是一个集合$X$，它有一个（Cech）闭包算子$u$，它不需要是幂等的。许多在拓扑空间中成立的性质在Cech闭包空间中也成立。在Cech闭包空间之间的连续函数集合上引入了真拓扑（分裂拓扑）和容许拓扑（联合连续拓扑）的概念.它表明，一些著名的结果Arens和Dugundji和Iliadis和Papadopoulos是正确的，在这种设置。我们强调定理1- 10包含了A. di Concilio和Georgiou与Papadopoulos的结果，证明了类连续函数空间为$θ$ -连续、强和弱$θ$ -连续、弱和超连续.
英文摘要：
A Cech closure space $(X,u)$ is a set $X$ with a (Cech) closure operator $u$ which need not be idempotent. Many properties which hold in topological spaces hold in Cech closure spaces as well. The notions of proper (splitting) and admissible (jointly continuous) topologies are introduced on the sets of continuous functions between Cech closure spaces. It is shown that some well-known results of Arens and Dugundji and of Iliadis and Papadopoulos are true in this setting. We emphasize that Theorems 1--10 encompass the results of A. di Concilio and of Georgiou and Papadopoulos for the spaces of continuous-like functions as $θ$-continuous, strongly and weakly $θ$-continuous, weakly and super-continuous.
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