Connectedness and Continuous Sequences in Finite Topological Spaces
نویسنده
چکیده
In this paper F1 denotes a non empty finite topology space and A, B, C denote subsets of F1. Let us consider F1. One can check that ∅(F1) is connected. We now state two propositions: (1) For all subsets A, B of F1 holds (A ∪ B) b = A ∪ B. (2) (∅(F1)) b = ∅. Let us consider F1. Observe that (∅(F1)) b is empty. Next we state the proposition (3) Let A be a subset of F1. Suppose that for all subsets B, C of F1 such that A = B ∪C and B 6= ∅ and C 6= ∅ and B misses C holds B meets C and B meets C. Then A is connected.
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