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June 1992 Fibrewise convergence and exponential laws
Seok Jong Lee, Kyung Chan Min
Tsukuba J. Math. 16(1): 53-62 (June 1992). DOI: 10.21099/tkbjm/1496161829

Abstract

We show that the category $\mathbf{Conv_{B}}$ of convergence spaces over $B$ is a convenient category for any $B \in \mathbf{Conv}$ . It is shown that without any condition on spaces the category $\mathbf{Conv_{B}}$ and the category $\mathbf{Conv_{B}^{B}}$ of sectioned convergence spaces over $B$ hold various exponential laws in a natural way. In $\mathbf{Conv_{B}}$, we can construct exponential object in terms of function spaces. Our fibrewise mapping space structure generalizes the fibrewise compact-open topology in some case.

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Seok Jong Lee. Kyung Chan Min. "Fibrewise convergence and exponential laws." Tsukuba J. Math. 16 (1) 53 - 62, June 1992. https://doi.org/10.21099/tkbjm/1496161829

Information

Published: June 1992
First available in Project Euclid: 30 May 2017

zbMATH: 0783.18005
MathSciNet: MR1178664
Digital Object Identifier: 10.21099/tkbjm/1496161829

Rights: Copyright © 1992 University of Tsukuba, Institute of Mathematics

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Vol.16 • No. 1 • June 1992
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