[Convergence spaces](https://ncatlab.org/nlab/show/convergence+space#definitions) are a generalization of topological spaces; we denote the category of convergence spaces with continuous maps with ${\bf Conv}$. Is ${\bf Conv}$ [cartesian-closed](https://en.wikipedia.org/wiki/Cartesian_closed_category)?



Is the category of convergence spaces cartesian-closed?
There seemed to be several slightly different notions of convergence spaces that were considered extensively in the 70ies. So I apologize if the following references do not actually answer your question (because I am missing some subtle differences between the definitions used in the papers below and the definition you linked to). 


For the convergence spaces of Cook and Fischer, Theorem 5 in the following paper should prove that they are cartesian closed: 


* H.R. Fischer and C.H. Cook. On Equicontinuity and Continuous Convergence. Math. Ann. 159 (1965), pp. 94-104. [(available here)](https://eudml.org/doc/182674)


For a slightly different notion of convergence, the $L\ast$-spaces, there is the following paper: 


* G.A. Edgar. A Cartesian closed category for topology.
General Topology and Appl. 6 (1976), no. 1, 65–72. [(available here)](http://www.sciencedirect.com/science/article/pii/0016660X7690009X)


There are also uniform convergence spaces, cartesian closed by the following paper: 


* R.S. Lee. The category of uniform convergence spaces is Cartesian closed.
Bull. Austral. Math. Soc. 15 (1976), no. 3, 461–465, 
DOI: [10.1017/S0004972700022905](https://doi.org/10.1017/S0004972700022905).


