Abstract
The notion of an almost fully closed mapping, which generalizes the definition of a fully closed map, is introduced. It is shown that the composition of almost fully closed mappings of compacta with the first axiom of countability is also almost fully closed, and so is the limit of a countable inverse transfinite sequence of the same mappings. A class of quasi- $F$ - compacta (which contains the class of Fedorchuk compacta ) is defined. For this class, some statements are proved that generalize and strengthen the known theorems on $F$ - compacta .
Highlights
The notion of an almost fully closed mapping, which generalizes the definition of a fully closed map, is introduced
It is shown that the composition of almost fully closed mappings of compacta with the first axiom of countability is almost fully closed, and so is the limit of a countable inverse transfinite sequence of the same mappings
A class of quasi-F -compacta is defined
Summary
The notion of an almost fully closed mapping, which generalizes the definition of a fully closed map, is introduced. В их числе теорема 1, утверждающая, что произведение квази-F -компактов Z1, Z2 не может быть квази-F -компактом счетной спектральной высоты, если qsh(Zi) = γi и для каждого i = 1, 2 существует ординал γi − 3. Оказывается, что такое же утверждение справедливо и для почти вполне замкнутых отображений (теорема 2).
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