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Screening properties of the subbase of all closed connected subsets of a connectedly generated space

1970
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Canadian Journal of Mathematics - Journal Canadien de Mathematiques
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Introduction. In [1] de Groot has introduced the notation "connectedly generated" (or eg) for those spaces in which the closed connected sets form a subbase for the topology. He pointed out that these are the semi-locally connected spaces of Whyburn. See [5; 6]. If X is eg, then, since X is closed, X is the union of a finite number of closed connected sets and, thus, has only a finite number of components. If p is any point in a eg space, and N v is any neighbourhood of p, then the complement

doi:10.4153/cjm-1970-075-0
fatcat:6wazi36jh5d5pkmqpw2lljnrvm