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In the paper there are invesigated the core topology, \(\tau_1\), the directional topology, \(\tau_2\), the Klee topology, \(\tau_3\), and the finite topology, \(\tau_0\), as well as the generalizations \(\tau_1(n)\), \(\tau_2(n)\) and \(\tau_3 (n)\) of \(\tau_1 ), \(\tau_2\) and \(\tau_3\), respectively. These generalizations are obtained when in the definition of a given topology the condition concerning...
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