F-door spaces and F-submaximal spaces
F-door spaces and F-submaximal spaces
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DOI：
10.4995/agt.2013.1621
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发表时间：
2013-04
影响因子：
0.8
通讯作者：
Lobna Dridi;Sami Lazaar;Tarek Turki
中科院分区：
文献类型：
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作者：
Lobna Dridi;Sami Lazaar;Tarek Turki
次极大空间和门空间在拓扑学中起着神秘的作用。在本文中，为了加强这一作用，我们致力于达到两个主要目标：第一个目标是刻画拓扑空间X，使得F(X)是从自顶到自范畴中的某个协变函子FF的次极大空间(对门空间)。T0和FH函子进行了全面的研究。其次，我们的兴趣指向由范畴集中的流(X，f)给出的映射f的刻划，使得(X，P(F))是次极大的(分别为门)，其中P(F)是X上的一个拓扑，其闭集恰好是f-不变集。
Submaximal spaces and door spaces play an enigmatic role in topology. In this paper, reinforcing this role, we are concerned with reaching two main goals: The first one is to characterize topological spaces X such that F(X) is a submaximal space (resp., door space) for some covariant functor Ff rom the category Top to itself. T0, and FH functors are completely studied. Secondly, our interest is directed towards the characterization of maps f given by a flow (X, f) in the category Set, such that (X,P(f)) is submaximal (resp., door) where P(f) is a topology on X whose closed sets are exactly the f-invariant sets.