Titlebook: Counterexamples in Topology; Lynn Arthur Steen,J. Arthur Seebach Book 1978Latest edition Springer-Verlag New York Inc. 1978 Compactificati

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Conjectures and Counterexamplesint set topology. Alexandroff and Urysohn [6] provided one solution as early as 1923 by imposing special conditions on a sequence of open conversing. Nearly ten years later R.L. Moore chose to begin his classic text on the Foundations of Point Set Theory [82] with an axiom structure which was a slig

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Technologietransfer und KulturkonfliktIt is often desirable for a topologist to be able to assign to a set of objects a topology about which he knows a great deal in advance. This can be done by stipulating that the topology must satisfy axioms in addition to those generally required of topological spaces.

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Technologietransfer und KulturkonfliktConnectedness denies the existence of certain subsets of a topological space with the property that Ū ∩ . = ∅ and . ∩ . = ∅. Any two such subsets are said to be . in the space. Although this concept is logically related to the separation axioms, it examines the structure of topological spaces from the opposite point of view.

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General IntroductionA . is a pair (.,τ) consisting of a set . and a collection τ of subsets of ., called ., satisfying the following axioms:.The collection τ is called a . for .. The topological space (.,τ) is sometimes referred to as the . . when it is clear which topology . carries.

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Separation AxiomsIt is often desirable for a topologist to be able to assign to a set of objects a topology about which he knows a great deal in advance. This can be done by stipulating that the topology must satisfy axioms in addition to those generally required of topological spaces.

Control-Group

ConnectednessConnectedness denies the existence of certain subsets of a topological space with the property that Ū ∩ . = ∅ and . ∩ . = ∅. Any two such subsets are said to be . in the space. Although this concept is logically related to the separation axioms, it examines the structure of topological spaces from the opposite point of view.