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.
Citation
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
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