Abstract
A set K in a topological space X is said to be compact if and only if any collection [G] of open sets covering K (i.e., ∪G ⊃ K) has a finite subcollection also covering K.
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Bibliography
Bernard Bolzano, Abhandlungen der Königliche böhmuschen Gesellschaft der Wissenschaften, 1817.
Emil Borel, Sur quelques points de la théorie des functions, Annales scientifiques de U Ecole Normale Supérieure, vol. (3) 12 (1895), p. 51.
T. H. Hildebrandt, The Borel theorem and its generalizations, Bulletin of the American Mathematical Society, vol. 32 (1926), pp. 423–474.
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© 1979 Springer-Verlag New York Inc.
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Whyburn, G., Duda, E. (1979). Compact Sets and Bolzano-Weierstrass Sets. In: Dynamic Topology. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6262-3_4
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DOI: https://doi.org/10.1007/978-1-4684-6262-3_4
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