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Martin Sleziak
Martin Sleziak
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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)

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)

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.

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)

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)

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.

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)

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)

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.
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Matthias Wendt
Matthias Wendt
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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)

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)

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.