积空间中滤子的compactness测度：重新讨论CAP中的Kuratowski-Mrkowka
Measure of compactness for filters in product spaces: Kuratowski-Mròwka in CAP revisited
摘要：
第一作者在收敛逼近空间的背景下，介绍了集合族相对于一类滤子的紧性测度。我们刻画了各种各样的地图（类型的商地图，封闭的地图，和完美的地图的变种）作为那些尊重这种措施的紧凑性在一种形式或另一种。我们建立了一个产品定理的措施紧性，从而产生作为实例新的产品定理的空间和映射，新的产品特征的空间和映射，从而扩大现有的结果，从收敛空间的收敛途径空间。特别是，结果的Mrkenwka-Kuratowski型得到的，新的光现有的结果的方法空间。
英文摘要：
The first author introduced a measure of compactness for families of sets, relative to a class of filters, in the context of convergence approach spaces. We characterize a variety of maps (types of quotient maps, closed maps, and variants of perfect maps) as those respecting this measure of compactness under one form or another. We establish a product theorem for measure of compactness that yields as instances new product theorems for spaces and maps, and new product characterizations of spaces and maps, thus extending existing results from the category of convergence spaces to that of convergence approach spaces. In particular, results of the Mròwka-Kuratowski type are obtained, shedding new light on existing results for approach spaces.
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