Geodesic
Compact unions of closed subsets are closed and compact intersections of open subsets are open
Portugaliae mathematica, Tome 49 (1992) no. 4, pp. 403-409

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Keywords: compact unions, compact intersections 
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     author = {Nachbin, Leopoldo},
     title = {Compact unions of closed subsets are closed and compact intersections of open subsets are open},
     journal = {Portugaliae mathematica},
     pages = {403--409},
     publisher = {mathdoc},
     volume = {49},
     number = {4},
     year = {1992},
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     zbl = {0784.54002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PORMA_1992__49_4_115797/}
}
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Nachbin, Leopoldo. Compact unions of closed subsets are closed and compact intersections of open subsets are open. Portugaliae mathematica, Tome 49 (1992) no. 4, pp. 403-409. http://geodesic.mathdoc.fr/item/PORMA_1992__49_4_115797/