Publications
Papers
- Functions of Baire class one over a Bishop topology, in M. Anselmo et al. (Eds.) Beyond the Horizon of Computability, CiE 2020, Springer, Lecture Notes in Computer Science 12098, 215-227, 2020.
- Embeddings of Bishop spaces, Journal of Logic and Computation, exaa015, 2020, https://doi.org/10.1093/logcom/exaa015
- McShane-Whitney extensions in constructive analysis, Logical Methods in Computer Science, Volume 16, Issue 1, 2020, pp. 18:1-18:23.
- Dependent Sums and Dependent Products in Bishop's Set Theory, in P. Dybjer et. al. (Eds) TYPES 2018, LIPIcs, Vol. 130, Article No. 3, 2019 DOI 10.4230/LIPIcs.TYPES.2018.3 PDF
- Borel and Baire sets in Bishop Spaces, in F. Manea et. al. (Eds): Computing with Foresight and Industry - 15th Conference on Computability in Europe, CiE 2019,
LNCS 11558, Springer, 2019, 240-252
https://doi.org/10.1007/978-3-030-22996-2_21 PDF - Constructive uniformities of pseudometrics and Bishop topologies, Journal of Logic and Analysis 11:FT2, 2019, 1-44 https://doi.org/10.4115/jla.2019.11.FT2 PDF
- McShane-Whitney pairs, in J. Kari, F. Manea and I. Petre (Eds.): Unveiling Dynamics and Complexity, CiE 2017, LNCS 10307, 351-363, 2017, DOI:10.1007/978-3-319-58741-7-33.PDF
- A density theorem for hierarchies of limit spaces over separable metric spaces, in T. V. Gopal, G. Jäger, S. Steila (Eds.): TAMC 2017, Springer LNCS 10185, 484-498, 2017. DOI: 10.1007/978-3-319-55911-7-35.PDF
- Limit spaces with approximations, Annals of Pure and Applied Logic 167 (9):737-752, 2016, DOI: 10.1016/j.apal.2016.04.013.PDF
- A constructive function-theoretic approach to topological compactness,, in M. Grohe, E. Koskinen and N. Shankar (Eds.) Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS '16, New York, NY, USA, July 5-8, 2016, 605-614, DOI: 10.1145/2933575.2933582.PDF
- A direct constructive proof of a Stone-Weierstrass theorem for metric spaces, in A. Beckmann, L. Bienvenu and N. Jonoska (Eds.) Pursuit of the Universal, CiE 2016, Springer, LNCS 9709, 364-374, 2016, DOI: 10.1007/978-3-319-40189-8-37. PDF
- The Urysohn Extension Theorem for Bishop Spaces, in S. Artemov and A. Nerode (Eds.) Symposium on Logical Foundations in Computer Science 2016, LNCS 9537, Springer, 2016, 299-316, DOI: 10.1007/978-3-319-27683-0-21. PDF
- Completely Regular Bishop Spaces, in A. Beckmann, V. Mitrana and M. Soskova (Eds.) Evolving Computability, CiE 2015, LNCS 9136, Springer, 2015, 302-312, DOI: 10.1007/978-3-319-20028-6-31. PDF
- The Contrapositive of Countable Choice for Inhabited Sets of Naturals, Journal of Universal Computer Science, Vol. 18, No. 20, pp. 2879-2892, 2012, DOI: 10.3217/jucs-018-20-2879. PDF
- The role of the Fifth Postulate in the Euclidean construction of parallels , in E. Barbin, N. Stehlikova and C. Tzanakis (Eds.) History and Epistemology in Mathematics Education, Proc.of the 5th European Summer University Vydavatelsky servis, Plzen, 2008, 595-604.
- Brouwer's intuitionism as a self-interpreted mathematical theory , in R. Cantoral, F. Fasanelli, A. Garciadiego, R. Stein., C. Tzanakis (Eds.) Electronic Proceedings of the HPM 2008, History and Pedagogy of Mathematics, Mexico City, 14-18 July 2008.
ArXiv Papers
- Direct spectra of Bishop spaces and their limits 2019.
- McShane-Whitney extensions in constructive analysis 2018.
Habilitation Thesis
- Families of Sets in Bishop Set Theory, submitted 22.04.2020
PhD Thesis
- Constructive Topology of Bishop Spaces München: Univ. München, Fakultät für Mathematik, Informatik und Statistik (Diss.). xvi, 203 p. (2015).
- Preliminary review in zbMATH
Notes/Preprints
- Univalent typoids, 2019.
- A Yoneda lemma-formulation of the univalence axiom, 2019.
- Dependent sums and dependent products in Bishop's set theory, 2018.
- Constructive Combinatorics of Dickson's Lemma, 2017.
- Advances in the theory of computable functionals TCF+ due to its implementation, 2013.
- Minlog implementations within the theory of computable functionals TCF+ , 2013.
- The topology of the strong Scott condition, 2012.
Abstracts and Reports
- Bishop spaces: constructive point-function topology, in Mathematisches Forschungsinstitut Oberwolfach Report No. 52/2014, Mathematical Logic: Proof Theory, Constructive Mathematics, pp.26-27, DOI: 10.4171/OWR/2014/52
- On the Formal Constructive Theory of Computable Functionals TCF+ (with H. Schwichtenberg) accepted Abstract, CiE 2012.
- Topological characterization of the compact element of (Tc, ⊂) for any topological space (X, T) (with V. Grigorakis, A. Stamatakis), Abstracts of Papers presented to the A.M.S., 93T-06-05, 1993.
Editorial work
- Editorial, (with H. Leitgeb, P. Schuster and H. Schwichtenberg), IFCoLog Journal of Logics and their Applications, Special Issue Proof, Truth, Computation, Vol.3 No. 4, 513-515, 2016, ISBN 978-1-84890-219-0.
Zentralblatt MATH Reviews
- M. Hendtlass: Fixed point theorems in constructive mathematics
- M. Hendtlass and P. Schuster: Minima and best approximations in constructive analysis
- D. Normann: Experiments on an internal approach to typed algorithms in analysis
- N. Weaver: Intuitionism and the liar paradox
Mathematical Reviews
- J. Berger, G. Svindland: Convexity and unique minimum points
- J. Millson, C. Strasser: A logic for best explanations
- P. Osinenko, S. Streif: A constructive version of the extremum value theorem for spaces of vector-valued functions
- H. Diener, M. Hendtlass: Bishop's lemma
- D. Rinaldi, P. Schuster, D. Wessel: Eliminating disjunctions by disjunction elimination
- D. Bridges, M. Hendtlass, E. Palmgren: A constructive Examination of Rectifiability
- A. Mahboubi: An induction principle over real numbers
- C. Duguid: Graph theory and the identity of indiscernibles
- Vít Punčochář: Intensionalisation of Logical Operators
- A. G. Melnikov and K. M. Ng: Computable structures and operations on the space of continuous functions
Past work
- Brouwer's Fan Theorem (Master Thesis)
- Introduction to Banach Algebras and the Gelfand-Naimark theorems
Last modified: 30.06.2020