ON THETA-TIGHTNESS
ON THETA-TIGHTNESS
Summary: We define the \(\theta\)-tightness and \(\theta\)-bitightness of a topological space and give some results in connection with these notions. In particular we prove that for every subset \(A\) of an Urysohn space \(X\) it holds \(| [A]_ \theta | \leq | A|^{\text{bt}_ \theta (X)}\), where \([A]_ \theta\) denotes the smallest \(\theta\)-closed subset of \(X\) containing \(A\).
- University of Messina Italy
Lower separation axioms (\(T_0\)--\(T_3\), etc.), \(\theta\)-bitightness, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Cardinality properties (cardinal functions and inequalities, discrete subsets), \(\theta\)-tightness
Lower separation axioms (\(T_0\)--\(T_3\), etc.), \(\theta\)-bitightness, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), Cardinality properties (cardinal functions and inequalities, discrete subsets), \(\theta\)-tightness
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