Homepage of Bob Lowen

photo

Department of Mathematics and Computer Science

University of Antwerp
  Monographs
  • Lowen, R., Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad (250pp)
    Oxford Mathematical Monographs Oxford University Press (1997)
    AMS Featured Review (MR 98f:54002) pdf
  • Lowen, R., Index Analysis: Approach Theory at Work (500pp),
    Springer Monographs in Mathematics Springer London Heidelberg New York Dordrecht (2015)
  Selected Publications (since 1991)
  • R. Lowen, K. Robeys, Completions of products of metric spaces,
    Quarterly J. Math. Oxford, 43, 319-338 (1991)
  • H.L. Bentley, H. Herrlich, R. Lowen, Improving constructions in topology, in
    Category Theory at Work, Heldermann Verlag (1991)
  • R. Lowen, Cantor-connectedness revisited,
    Comment. Math. Univ. Carolinae, 33, 525-532 (1992)
  • R. Lowen, K. Robeys, Products of metric spaces,
    Mathematical Research Series, 67, 203-212, Akademie Verlag (1992)
  • R. Lowen, Approximation of weak convergence,
    Math. Nachrichten, 160, 299-312 (1993)
  • R. Lowen, K. Robeys, Compactifications of products of metric spaces and their relation to Smirnov and Cech-Stone compactifications,
    Topology Appl, 55, 163-183 (1994)
  • R. Lowen, M. Sioen, The Wijsman and Attouch-Wets topologies on hyperspaces revisited,
    Topology Appl., 70, 179-197 (1996)
  • R. Lowen, M. Sioen, Applications of approach theory in functional analysis,
    Topology Atlas, 1(1996) - Electronic
  • E. Colebunders, R. Lowen, F. Verbeeck, Exponential objects in the construct PRAP,
    Cahiers Top. Géom. Diff. Cat., 38, 259-276 (1997)
  • R. Lowen, M. Sioen, Proximal hypertopologies revisited.
    Set Valued Analysis, 6, 1-9 (1998)
  • Y.J. Lee, R. Lowen, Approach theory in merotopic, Cauchy and convergence spaces I & II,
    Acta Math. Hungar., 83, 189-207 & 209-229 (1999)
  • H. Herrlich, R. Lowen, On simultaneously reflective and coreflective subconstructs,
    G.C.L. Brummer Festschrift, Cape Town, University of Cape Town, 121-129 (1999)
  • R. Lowen, B. Windels, Approach groups,
    Rocky Mountain J. Math, 30(3), 1057-1073, (2000)
  • R. Lowen, M. Sioen, Weak representations of quantified hyperspace structures,
    Topology Appl, 104, 169-179 (2000)
  • R. Lowen, A. Verschoren, M. Soultan, Multivalued sheaf constructions,
    Comm. Algebra, 28, 719-736 (2000)
  • R. Lowen, M. Sioen, Approximations in functional analysis,
    Resultate der Mathematik, 37, 345-372 (2000)
  • R. Lowen, M. Sioen, A unified look at completion in Met, Unif and Ap,
    Appl. Categ. Structures, 8, 447-461 (2000)
  • R. Lowen, M. Sioen, A Wallman-Shanin compactification for approach spaces,
    Rocky Mt J. Mathematics, 30, 1381-1419 (2000)
  • E. Colebunders, R. Lowen, Supercategories of Top and the inevitable emergence of categorical topology,
    in Handbook of the History of General Topology Vol 3, 969-1026, Kluwer Academic Publishers (now Springer) (2001)
  • E. Colebunders, R. Lowen and M. Nauwelaerts, The cartesian closed hull of the category of Approach Spaces,
    Cahiers Topol. Géom. Diff. Cat., 42, 242-260 (2001)
  • R. Lowen, D. Vaughan, Completing quasi-metric spaces: an alternative approach,
    Houston J. Math, 29, 113-136 (2003)
  • R. Lowen, Approach spaces,
    in Encyclopedia of General Topology, North Holland, 293-298 (2003)
  • R. Lowen, An Ascoli theorem in approach theory,
    Topology Appl., 137, 207-213 (2004)
  • R. Lowen, M. Sioen, On the multitude of monoidal closed structures in UAP,
    Topology Appl., 137, 215-223 (2004)
  • R. Lowen, S. Verwulgen, Approach vector spaces,
    Houston J. Math., 30(4), 1127-1142 (2004)
  • B. Banaschewski, R. Lowen, A cancellation law in the categories of partially ordered sets and T0 spaces,
    Proceedings Amer. Math. Soc., 132, 3463-3466 (2004)
  • E. Colebunders, R. Lowen, P. Wuyts, A Kuratowski-Mrowka theorem in approach theory,
    Topology Appl., 153, 756-766 (2005)
  • G. Di Maio, R. Lowen, S.A. Naimpally, M. Sioen, Gap functionals, proximities and hyperspace compactification,
    Topology Appl., 153, 924-940 (2005)
  • E. Colebunders, R. Lowen, Metrically generated theories,
    Proceedings Amer. Math. Soc., 133, 1547-1556 (2005)
  • B. Banaschewski, R. Lowen, C. Van Olmen, Sober approach spaces,
    Topology Appl., 153, 3059-3070 (2006)
  • B. Banaschewski, R. Lowen, C. Van Olmen, Regularity in approach theory,
    Acta Math. Hung., 115(3), 183-196 (2007)
  • E. Colebunders, R. Lowen, E. Vandersmissen, Uniqueness of completeness in metrically generated theories,
    Topology Appl., 155, 39-55 (2007)
  • E. Colebunders, R. Lowen, Bornologies and metrically generated theories,
    Topology Appl., 156, 1224-1233, (2009)
  • R. Lowen, C. Van Olmen, T. Vroegrijk, Functional ideals and topological theories,
    Houston J. Math. Vol 34 nr 3 (2008) 1065-1089
  • R. Lowen, P. Wuyts, Stable subconstructs: a correction and new results
    Applied Categ. Structures 19, 2011, p. 539-555
  • R. Lowen, C. Van Olmen, Approach Theory, in Beyond Topology,
    Contemporary Mathematics Amer. Math. Soc. Vol 486, 2009, p. 305-323
  • R. Lowen, M. Sioen, S. Verwulgen, Categorical Topology, in Beyond Topology,
    Contemporary Mathematics Amer. Math. Soc. Vol 486, 2009, p. 1-36
  • E. Giuli, E. Colebunders, R. Lowen, Spaces modelled by an algebra on [0,\infty] and their complete objects,
    Topology Appl. 157, 2010, p. 1335-1346
  • B. Berckmoes, R. Lowen, J. Van Casteren, Approach theory meets probability theory,
    Topology Appl. 158, 2011, p. 836-852
  • B. Berckmoes, R. Lowen, J. Van Casteren, Distances on probability measures and random variables,
    J. Math. Anal. Appl. 374, 412-428 (2011)
  • E. Colebunders, R. Lowen, W. Rosiers, Lax algebras via initial monad morphisms: App, Top, Met and Ord
    Topology Appl. 158, 2011, p. 882-903
  • B. Banaschewski, R. Lowen, C. Van Olmen, Compactness in approach frames
    Order 29, 2012, 105-118 (doi:10.1007/s11083-011-9200-x)
  • E. Colebunders, S. De Wachter, R. Lowen, Intrinsic approach spaces on domains
    Topology Appl. 158, 2343–2355 (2011)
  • E. Colebunders, R. Lowen, A. Van Geenhoven, Local metrically generated theories
    Topology Appl. 159, 2320–2330, (2012)
  • R. Lowen, P. Wuyts, The Vietoris hyperspace revisited
    Acta Math. Hungarica 139 (3) (2013) 286-302
  • B. Berckmoes, R. Lowen, J. Van Casteren An isometric study of the Lindeberg-Feller CLT via Stein's method
    J. Math. Anal. Appl doi information: 10.1016/j.jmaa.2015.08.040 405 (2) (2013) 484-498
  • E. Colebunders, S. De Wachter, R. Lowen, Fixed points of contractive maps on DCPO's
    Mathematical Structures in Computer Science (doi) 10.1017/S0960129513000017
  • R. Lowen, S. Sagiroglu, Convex closures, weak topologies and feeble approach spaces
    Journal of Convex Analysis 21:2(2014), p. 581-600
  • R. Lowen, W. Tholen, Introduction to Monoidal Topology
    in Monoidal topology : a categorical approach to order, metric and topology Cambridge, Cambridge University Press, 2014, p. 1-17
  • Hofmann D., Lowen R., Lucyshyn-Wright R., Seal G.J..- Kleisli monoids
    in Monoidal topology : a categorical approach to order, metric and topology Cambridge, Cambridge University Press, 2014, p. 284-374
  • Colebunders E., Lowen R., Van Opdenbosch K., Regularity for relational algebras and the case of approach spaces,
    Topology Appl. 200 (2016) 79-100
  • B. Berckmoes, R. Lowen, J. Van Casteren Stein's Method and a Quantitative Lindeberg CLT for the Fourier Transforms of Random Vectors
    J. Math. Anal. Appl 433 (2016) 1441-1458, doi information: 10.1016/j.jmaa.2015.08.040
  • B. Berckmoes, R. Lowen A Note on Probability Metrics in a Categorical Setting
    Appl. Categ. Struct. , 24(5) (2016) 559-567 doi information: 10.1007/s10485-016-9448-9
  • L. Bentley, E. Colebunders, B. Lowen, et al.: In Memoriam Horst Herrlich,
    Appl. Categ. Struct. , 24 (5), (2016), 433-435
  • Colebunders E., Lowen R., Zero dimensionality of the Cech-Stone compactification of an approach space,
    Topology Appl. vol 273, (2020), 106973, doi 10.1016/j.topol.2019.106973
  • E. Colebunders, R. Lowen, M. Sioen, An isomorphism of the Wallman and Cech-Stone compactifications
    Quaestiones Math. (2021), doi.org 10.2989/16073606.2021.1891991 in press, early access may 2021.
  • E. Colebunders, R. Lowen, Supported approach spaces
    Quaestiones Math. 46,(2023), 161-190
  • E. Colebunders, R. Lowen, Approximation and compactness
    (2024) submitted for publication
  Preprint, submitted or in preparation
  • E. Colebunders, R. Lowen, Generated approach spaces (in preparation)
  Books as editor
  • Aull, C., Lowen, R. (Editors), Handbook of the History of General Topology , Volume 1 (400pp)
    Kluwer Academic Publishers (1997)
  • Aull, C., Lowen, R. (Editors), Handbook of the History of General Topology , Volume 2 (400pp)
    Kluwer Academic Publishers (1998)
  • Aull, C., Lowen, R. (Editors), Handbook of the History of General Topology , Volume 3 (400pp)
    Kluwer Academic Publishers (2001)
  • Lowen R., Verschoren A. (Editors) Foundations of Generic Optimization, Volume 1
    Springer (2005)
  • Lowen R., Verschoren A. (Editors) Foundations of Generic Optimization, Volume 2
    Springer (2007)
  Promotor of PhD theses
  • Kristin Robeys, University of Antwerp, RUCA, Extensions of Products of Metric Spaces, 1992.
    Adviser R. Lowen.
  • Rony Baekeland, University of Brussels, VUB, Measures of compactness and their application to convergence of probability measures, 1992.
    Adviser R. Lowen, Co-adviser E. Colebunders (VUB).
  • Nieves Blasco, University of Antwerp, RUCA, Compactification and convergence-supercategories of FNS, 1995.
    Adviser R. Lowen.
  • Bart Windels, University of Antwerp, RUCA, Uniform Approach Theory, 1997.
    Adviser R. Lowen.
  • Mark Sioen, University of Antwerp, RUCA, Extension Theory for Approach Spaces, 1997.
    Adviser R. Lowen.
  • Werner Peeters, University of Antwerp, RUCA, Semi-pseudo-metric and Pretopological Methods in Image Analysis, 1999.
    Adviser R. Lowen.
  • Tim Daniels, University of Antwerp, RUCA, Asymptotic behaviour of queuing systems, 1999.
    Adviser C. Blondia, Co-adviser R. Lowen.
  • Francis Verbeeck, University of Antwerp, RUCA, The Category of Pre-approach Spaces, 2000.
    Adviser R. Lowen, Co-adviser E. Colebunders (VUB).
  • Mark Nauwelaerts, University of Antwerp, RUCA, Categorical Hulls in Approach Theory, 2000.
    Adviser R. Lowen.
  • Stijn Verwulgen, University of Antwerp, UA, A Categorical Approach to Quantified Functional Analysis, 2003.
    Adviser R. Lowen, Co-adviser M. Sioen (VUB).
  • Christophe Van Olmen, University of Antwerp, UA, A study of the interaction between Frame Theory and Approach Theory, 2005.
    Adviser R. Lowen.
  • Vandersmissen Eva, University of Brussels, VUB, Firm completions in metrically generated constructs, 2008.
    Adviser E. Colebunders, Co-adviser R. Lowen
  • Tom Vroegrijk, University of Antwerp, UA, Bornological structures in approach theory and metrically generated theories, 2009.
    Adviser R. Lowen.
  • Anneleen Van Geenhoven, University of Antwerp, UA, Local metrically generated theories, 2010.
    Adviser R. Lowen
  • Wannes Rosiers, University of Antwerp, UA, Topological theories in a lax-algebraic setting, 2011.
    Adviser R. Lowen
  • Ben Berckmoes, University of Antwerp, UA, Approach structures in probability theory, 2014.
    Adviser R. Lowen
  • Karen Van Opdenbosch, "Twin-PhD" University of Brussels-University of Antwerp, Approach Theory and Monoidal Topology , 2019.
    Adviser E. Colebunders, Co-adviser R. Lowen