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Alexander duality for parametrized homology
Kališnik Verovšek, Sara, 1986-
Parametrizirana homologija je različica cik-cak vztrajne homologije, ki meri, kako se homologija nivojnic parametriziranega prostora spreminja s parametrom. V članku predstavimo parametrizirano ...različico Aleksandrove dualnosti. Naj bo ▫$X \subset \mathbb{R}^n \times \mathbb{R}$▫ z ▫$n \geq 2$▫ kompaktna množica, ki ustreza določenim pogojem, ▫$Y = (\mathbb{R}^n \times \mathbb{R}) \setminus X$▫ in naj bo ▫$p$▫ projekcija na drugo komponento. Prostora ▫$X$▫ in ▫$Y$▫, opremljena z dano projekcijo, sta parametrizirana prostora. Dokažemo: če ima ▫$(X, p|_X)$▫ dobro definirano parametrizirano homologijo, potem ima par ▫$(Y, p|_Y)$▫ dobro definirano parametrizirano reducirano homologijo. Vzpostavimo zvezo med parametrizirano homologijo ▫$(X, p|_X)$▫ in parametrizirano reduciranohomologijo ▫$(Y, p|_Y)$▫.
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