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Multicoherence of spaces of the form $ X/M$


Author: Alejandro Illanes M.
Journal: Proc. Amer. Math. Soc. 101 (1987), 190-194
MSC: Primary 54F55
DOI: https://doi.org/10.1090/S0002-9939-1987-0897093-8
MathSciNet review: 897093
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Abstract: Let $ X$ be a connected, locally connected, normal $ {T_1}$-space and let $ M$ be a closed connected, locally connected subspace of $ X$. Suppose that $ X/M$ denotes the space obtained by identifying $ M$ in a single point, and that, for a connected space $ Y$, $ \imath (Y)$ denotes the multicoherence degree of $ Y$. In this paper, we prove that if $ M$ is unicoherent, then $ \imath (X) = \imath (X/M)$. As an application of this result we prove that if $ X = A \cup B$, where $ A,B$ are closed subsets of $ X$ and $ A \cap B$ is connected, locally connected and unicoherent, then $ \imath (X) = \imath (A) + \imath (B)$. Also, we prove that if $ X/M$ is unicoherent, then $ \imath (X) \leqslant \imath (M)$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1987-0897093-8
Keywords: Multicoherence, unicoherence, identifications
Article copyright: © Copyright 1987 American Mathematical Society

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