On the way to Frölicher bornology

References

• B. Aqzzouz, The ε∞-product of b-space by a quotient bornological space, Methods of Functional Analysis and Topology 13 (2007), 211–222.
   Google Scholar
• A. Batubenge, Symplectic Frölicher spaces of constant dimension, Ph.D. thesis, University of Cape Town, Cape Town, 2004.
   Google Scholar
• A. Batubenge, A survey on Frölicher spaces, Quaestiones Mathematicae 38(6) (2015), 869–884. doi: 10.2989/16073606.2014.981740
   Web of Science ®Google Scholar
• A. Batubenge, P. Iglesias-Zemmour, Y. Karshon, and J. Watts, Diffeological, Frölicher, and Differential Spaces, arXiv:1712.04576v1 [math.DG], 13 Dec 2017.
   Google Scholar
• A. Batubenge and P. Ntumba, On the way to Frölicher Lie groups, Quaestiones Mathematicae 28 (2005), 73–93. doi: 10.2989/16073600509486116
   Google Scholar
• A. Batubenge and P. Ntumba, Characterization of Vector Fields on the Frölicher Standard n-Simplex Imbedded in ℝn, and Hamiltonian Formalism on Differential Spaces, Quaestiones Mathematicae 32 (2009), 71–90. doi: 10.2989/QM.2009.32.1.7.709
   Web of Science ®Google Scholar
• A. Batubenge and H. Tshilombo, Topologies and smooth maps on initial and final objects in the category of Frölicher spaces, Demonstratio Math. 42 (2009), 641–655.
   Google Scholar
• A. Batubenge and H. Tshilombo, Topologies on product and coproduct Frölicher spaces, Demonstratio Math. 47 (2014), 1012–1024.
   Google Scholar
• A. Batubenge and H. Tshilombo, Notes on pre-Frölicher spaces, Quaestiones Mathematicae 39(8) (2016), 1115–1129. doi: 10.2989/16073606.2016.1261953
   Web of Science ®Google Scholar
• G. Beer, On Metric Boundedness Structures, Set-valued Anal. 7 (1999), 195–208. doi: 10.1023/A:1008720619545
   Google Scholar
• G. Beer, Embeddings of bornological universes, Set-valued Anal. 16 (2008), 477–488. doi: 10.1007/s11228-007-0068-2
   Google Scholar
• G. Beer and M. Garrido, Bornologies and Locally Lipschitz Functions, Bull. Aust. Math. Soc. 90 (2014), 257–1233. doi: 10.1017/S0004972714000215
   Web of Science ®Google Scholar
• G. Beer and S. Levi, Total boundedness and bornologies, Topology and its Applications, 156(7) (2009), 1271–1288. doi: 10.1016/j.topol.2008.12.030
   Web of Science ®Google Scholar
• F. Borceux, On Bornological Semi-Abelian Algebras, Categories and General Algebraic Structures with Applications 14(1) (2021), 181–222. doi: 10.29252/cgasa.14.1.181
   Web of Science ®Google Scholar
• J. Borwein, M. Fabian, and J. Vanderweiff, Locally Lipschitz functions and bornological derivatives, arXiv.math/9302211v1 [math.FA], 1993.
   Google Scholar
• P. Cherenack, Smooth Homotopy, Topology with Applications, (Edited by A. Szekszárd, 1993, Hungary), Bolyai Society Mathematical Studies, Vol. 4, pp. 47–70, Jänos Bolya Mathematical Society, Budapest, 1995.
   Google Scholar
• P. Cherenack, Applications of Frölicher spaces to cosmology, Annals Univ. Sc. Budapest 41 (1998), 63–91.
   Google Scholar
• P. Cherenack, Frölicher versus Differential Spaces: A prelude to cosmology, In: Papers in Honour of Bernhard Banaschewski, (G. Brümmer and C. Gilmour, eds.), pp. 391–413, Kluwer Academic Publishers, Dordrecht, 2000.
   Google Scholar
• P. Cherenack, Distribution via Seminorms and Frölicher spaces, Steps in Differential Geometry, Proceedings of the Colloquium on Differential Geometry held at Debrecen, Hungary, 25–30 July 2000. The European Mathematical Information Service, pp. 85–93, (link: https://www.emis.de/proceedings/CDGD2000/contents.html), 2000.
   Google Scholar
• P. Cherenack and P. Multarzyński, Smooth Exponential Objects and Smooth Distributions, preprint, 2000.
   Google Scholar
• P. Cherenack and P. Ntumba, Spaces with Differential Structure and an Application to Cosmology, Demonstratio Mathematica XXXIV(1) (2001), 161–180.
   Google Scholar
• E. Colebunders and R. Lowen, Bornologies and metrically generated theories, Topology and its Applications 156(7) (2009), 1224–1233. doi: 10.1016/j.topol.2008.12.018
   Web of Science ®Google Scholar
• B. Dugmore, A Framework for Homotopy Theory and Differential Geometry in the category of Frölicher spaces, Ph.D. thesis, University of Cape Town, Cape Town, 1999.
   Google Scholar
• B. Dugmore and P. Ntumba, On Tangent Cones of Frölicher Spaces, Quaestiones Mathematicae 30(1) (2007), 67–83. doi: 10.2989/160736007780205747
   Web of Science ®Google Scholar
• A. Frölicher, Catègories cartásiennement fermées engendrées par des monoïdes, Cahiers de Topologie et Géométrie Différentielle Catégoriques 21(4) (1980), 367–375.
   Google Scholar
• A. Frölicher, Applications lisses entre espaces et variétés de Fréchet, C.R. Acad. Sci. Paries 293(1) (1981), 125–127.
   Google Scholar
• A. Frölicher, Cartesian closed categories and analysis of smooth maps, Categories in Continuum Physics: Lectures given at a Workshop held at SUNY, Buffalo 1982, pp. 43–51, Springer, Berlin, 1986.
   Google Scholar
• A. Frölicher, Smooth structures, Category Theory, Gummersbach, 1981, Lecture Notes in Math., Vol. 962, pp. 69–81, Springer, Berlin/New York, 1982.
   Google Scholar
• A. Frölicher and A. Kriegl, Linear spaces and differentiation theory, Wisley and Sons, Chichester, 1988.
   Google Scholar
• A. Frölicher and A. Kriegl, Topology and Differentiation Theory, In: Recent Progress in General Topology, pp. 216–232, Elsevier, Amsterdam, 1992.
   Google Scholar
• P. Garcia, A. Perez-Rendón, and J. Souriau, Groupes Differentiels, Lecture Notes in Mathematics, Vol. 1174, pp. 91–128, Springer, New York, 1980.
   Google Scholar
• H. Hogbe-Nlend, Bornologies and functional analysis, North-Holland Publishing Company, Amsterdam, 1977.
   Google Scholar
• S-T. Hu, Boundedness in a Topological Space, J. Math Pares Appl. 228 (1949), 287–320.
   Google Scholar
• A. Kriegl and P. Michor, The convenient setting of Global Analysis, Mathematical Surveys and Monographs, Vol. 53, American Mathematical Society, Providence, RI, 1997.
   Google Scholar
• J. Lawvere, S. Schanuel, and W. Zane, On C∞-functions, Preprint, State University of New York, Buffalo, 1981.
   Google Scholar
• A. Lechinki and S. Levi, Bornological convergences, J. Math Anal. Appl. 297 (2004), 751–770. doi: 10.1016/j.jmaa.2004.04.046
   Web of Science ®Google Scholar
• R. Meyer, Bornological versus Topological Analysis in Metrizable Spaces, arXiv:math/0310225v2 [math.FA], 9 Feb. 2004.
   Google Scholar
• S Özcay, Bornologies and bitopological function spaces, University of Nis, Faculty of Sciences and Mathematics, Filomat 27(7) (2013), 1345–1349. doi: 10.2298/FIL1307345O
   Web of Science ®Google Scholar
• R. Sikorski, Abstract Covariant Derivative, Colloq. Math. 18 (1967), 251–272. doi: 10.4064/cm-18-1-251-272
   Web of Science ®Google Scholar
• R. Sikorski, Differential Modules, Colloq. Math. 24 (1971), 45–79. doi: 10.4064/cm-24-1-45-79
   Web of Science ®Google Scholar
• J. Smith, The De Rham Theorem for General Smooth Spaces, Tôhoku Math. Journ. 18(2) (1966), 115–137. doi: 10.2748/tmj/1178243443
   Google Scholar
• A. Šostak and I. Uljane, Bornological Structures on Many-valued Sets, Rad Hazu. Mathematičke Znanosti 21(532) (2017), 143–168.
   Google Scholar
• J. Souriau, Groupes Differentiels, Differential Geometric Methods in Mathematical Physics, Proceedings of the Conferences held in Aix-en-Provence/Salamanca, September 1979, pp. 91–128, Springer, Berlin, 1979.
   Google Scholar
• A. Stacey, Comparative smootheolgy, arXiv:0802.2225v2 [math.DG], 21 May 2010.
   Google Scholar