# Ľubica Holá

## (doc. RNDr. Ľubica Holá, DrSc.)

Curriculum Vitae | List of Publications

## Curriculum Vitae:

- I was born at September 15, 1958 at Handlová.
- In 1982 I graduated in mathematical analysis at the Faculty of Mathematics and Physics, Comenius University.

### Career:

- In 1989 I started my PhD study under the supervision of Professor Neubrunn and
- in 1991 I finished it.
- In 1993 I took the degree of Associative Professor.
- In 2004 I submitted my disertation Topologies on function spaces and hyperspaces.
- In 2005 I took the degree DrSc.

In 1993 my research project devoted to the study of hyperspace topologies was aworded by Italian CNR by 10-monthly stay at University of Milan under the supervision of Professor Lucchetti.

My research is devoted to the study of topologies on function spaces, hyperspaces and also to the study of set-valued mappings and generalized continuity of mappings. My recent research deals with minimal usco (cusco) maps and their selections and with topologies of strong uniform convergence on bornologies.

Up to now I published 82 papers. My papers have more than 200 citations.

**Invited research stays:** Milano, Napoli, Praha, Caserta, Perugia, Padova, Berne, Pembroke, Youngstown.

Up to now I received 20 invitations to deliver a lecture on International Conferences.

### List of Publications:

- Ľ. Holá, I. Kupka, Closed graph and open mapping theorems for linear relations, Acta Math. Univ. Comenianae 46/47 (1985), 157-162.
- Ľ. Holá, P. Maličký, Continuous linear selectors of linear relations, Acta Math. Univ. Comenianae 48/49 (1986), 153-157.
- V. Baláž, Ľ. Holá, T. Neubrunn, Remarks on c-upper semicontinuous multifunctions, Acta Mat. Univ. Comenianae 50/51 (1987), 159-165.
- Ľ. Holá, Some conditions that imply continuity of almost continuous multifunctions, Acta Mat. Univ. Comenianae 52/53 (1987), 159-165.
- Ľ. Holá, A remark on the theory of sets of distances, Acta Mat. Univ. Comenianae 52/53 (1987), 167-175.
- Ľ. Holá, Relations approximated by continuous functions in the Hausdorff metric, Acta Univ. Carolinae Math. et. Phys. 28 (1987), no 2, 67-72.
- Ľ. Holá, Almost continuous functions, Rend. Circ. Palermo 14 (1987), 329-333.
- Ľ. Holá, T. Šalát, Graph convergence, uniform, quasiuniform and continuous convergence and some characterizations of compactness, Acta Math. Univ. Comenianae 54/55 (1988), 121-132.
- Ľ. Holá, An extension theorem for multifunctions and a characterization of complete metric spaces, Math. Slovaca 38 (1988), 177-182.
- Ľ. Holá, Remark on almost continuous multifunctions, Math. Slovaca 38 (1988), 325-331.
- Ľ. Holá, An extension theorem for continuous functions, Czech. Math. J. 38 (1988), 398-403.
- Ľ. Holá, T. Neubrunn, On almost uniform convergence and convergence in Hausdorff metric, Radovi Mat. 4 (1988), 193-205.
- Ľ. Holá, Most of optimization problems have unique solution, C. R. Acad. Bulg. 42 (1989), 5-8.
- Ľ. Holá, Hausdorff metric convergence of continuous functions, Proc. Sixth Prague Top. Symp. Verlag, Berlin (1988), 263-271.
- Ľ. Holá, T. Neubrunn, Hausdorff metric convergence of functions and its relation to the convergence in measure, Proc. of the First Winter School on Measure Theory, Liptovský Ján (1988), 40-45.
- Ľ. Holá, On determining sets for the class of somewhat continuous functions, Math. Slovaca 39 (1989), 257-259.
- Ľ. Holá, P. Kostyrko, T. Powell, T. Šalát, Mean value theorem and Lagrange sets of real functions, Acta Mat. Univ. Comenianae 58/59 (1990), 77-93.
- Ľ. Holá, T. Neubrunn, Hausdorff distance and the structure of certain function spaces, Math. Balcanica 4 (1990), 61-68.
- Ľ. Holá, Functional characterizations of Baire spaces, Proc. Amer. Math. Soc. 109 (1990), 4, 1121-1124.
- Ľ. Holá, The Attouch-Wets topology and a characterization of normable linear spaces, Bull. Austral. Math. Soc. 44 (1991), 11-18.
- Ľ. Holá, T. Neubrunn, Functions vanishing at infinity, Radovi Mat. 7 (1991), no 1, 185-189.
- Ľ. Holá, Hausdorff metric on the space of upper semicontinuous multifunctions, Rocky Mountain J. of Math. 22, no 2 (1992), 601-610.
- Ľ. Holá, R.A. McCoy, The Fell topology on C(X), Proc. 1990 Conf. on General Topology and Appl., Long Island University, New York Acad. Sci. (1992), 99-110.
- Ľ. Holá, Topologies on graphs of linear functionals, Topology, measure and fractals, Akademie Verlag, Berlin (1992), 198-207.
- Ľ. Holá, D. Holý, Further characterizations of boundedly UC spaces, CMUC 34, 1 (1993), 175-183.
- Ľ. Holá, D. Holý, A weakening of the Attouch-Wets topology on function spaces, Tatra Mountains Mathematical Publications 2 (1993), 105-121.
- Ľ. Holá, R.A. McCoy, Functions with closed graphs, Kobe J. Math. 10 (1993), 117-124.
- G. Di Maio, Ľ. Holá, Hypertopologies on function spaces, Rend. Circ. Palermo XLII (1994), 83-97.
- G. Di Maio, Ľ. Holá, D. Holý, Attouch-Wets topology on function spaces, Boll. U.M.I. (7), 9-A (1995), 259-272.
- Ľ. Holá, R. Lucchetti, Equivalence among hypertopologies, Set-Valued Analysis 3 (1995), 339-350.
- G. Di Maio, Ľ. Holá, On hit-and-miss topologies, Rend. Ac. Sc. Fis. Mat. Napoli, 62 (1995), 103-124.
- Ľ. Holá, R. Lucchetti, Polishness of weak topologies generated by gap and excess functionals, Journal of Convex Analysis 3 (1996), 283-294.
- Ľ. Holá, The Wijsman topology as a weak topology generated by gap functionals determined by families of noncompact sets Boll. U.M.I. (7) 10-A (1996), 51-62.
- Ľ. Holá, J. Tóth, L. Zsilinszky, The generic property of non-expansive mappings in Banach spaces, Rivista di Matematica Pura ed Applicata 17 (1996), 63-69.
- G. Di Maio, Ľ. Holá, Wijsman topology on function spaces, Rend. Circ. Palermo 46 (1997), 52-70.
- Ľ. Holá, D. Holý, E. Meccariello, Wijsman topology on lower semicontinuous functions, Boll. U.M.I. (7) 11-B (1997), 973-986.
- G. Di Maio, Ľ. Holá, A hypertopology determined by the family of totally bounded sets is the infimum of upper Wijsman topologies, Questions and Answers in General Topology, 15 (1997), 51-66.
- G. Di Maio, Ľ. Holá, D. Holý, A characterization of locally compact spaces by epiconvergence and convergence in epitopology, Questions and Answers in General Topology, 15 (1997), 245-257.
- Ľ. Holá, Coincidence of Vietoris and Wijsman topologies: a new proof, Serdica 1 (1997), 1-4.
- Ľ. Holá, S. Levi, Decomposition properties of hyperspace topologies, Set-Valued Analysis 5 (1997), 309-321.
- G. Di Maio, Ľ. Holá, D. Holý, R.A. McCoy, Topologies on continuous functions, Topology and its Applications 86 (1998), 105-122.
- Ľ. Holá, Uniformizability of generalized compact-open topology, Tatra Mountains Math. Publ. 14 (1998), 219-224.
- P. Brandi, R. Ceppitelli, Ľ. Holá, Topological properties of a new graph topology, Journal of Convex Analysis 5 (1998), No 2, 1-12.
- Ľ. Holá, Complete metrizability of generalized compact-open topology, Topology and its Applications 91 (1999), 159-167.
- Ľ. Holá, S. Levi, J. Pelant, Normality and paracompactness of the Fell topology, Proc. Amer. Math. Soc. 127 (1999), 2193-2197.
- Ľ. Holá, H.P. Kunzi, Properties related to compactness in hyperspace topologies, Topology Proceedings 23 (1998), 191-205.
- P. Brandi, R. Ceppitelli, Ľ. Holá, Kuratowski convergence on compacta and Hausdorff metric convergence on compacta, Comment. Math. Univ. Carolinae 40,2 (1999), 309-318.
- G. Di Maio, Ľ. Holá, E. Meccariello, Notes on hyperspace topologies, Rostock Math. Kolloq. 52, (1998), 19-32.
- Ľ. Holá, H. Poppe, Fell topology on the space of functions with closed graphs, Rend. Circ. Palermo, Serie II, Tomo XLVIII (1999), 419-430.
- Ľ. Holá, R.A. McCoy, Compactness in the fine and related topologies, Topology and its Applications 109 (2001), 183-190.
- Ľ. Holá, L. Zsilinszky, Completness type properties of the space of partial maps with closed domains, Topology and its Applications 110 (2001), 303-321.
- Ľ. Holá, Topologies on partial maps, Quaderni di Matematica, 3 (1998), 157-185.
- Del Prete, M. Di Iorio, Ľ. Holá, Graph convergence of set-valued maps and its relationship to other convergences, Journal of Applied Analysis 6, No. 2 (2000), 213-226.
- Bouziad, Ľ. Holá, L. Zsilinszky, On hereditary Bairness of the Vietoris topology, Topology and its Applications 115 (2001), 247-258.
- G. Di Maio, Ľ. Holá, J. Pelant, Properties related to the first countability of hyperspace topologies, Q and A in General Topology 19 (2001), 139-157.
- G. Di Maio, Ľ. Holá, E. Meccariello, Some compactness properties in hyperspaces: A new approach, Topology and its Applications 137, (2004), 83-47.
- Ľ. Holá, A note on proximal graph topology, Q and A in General Topology 20 (2002), 45-47.
- Ľ. Holá, Spaces of densely continuous forms, usco and minimal usco maps, Set-Valued Analysis, 11, (2003), 133-151.
- Ľ. Holá, J. Pelant, Recent progress in hyperspaces, Chapter 10 in "Recent progress in general topology", North Holland, Elsevier 2002, 253-285.
- Ľ. Holá, J. Pelant, L. Zsilinszky, Developable hyperspaces are metrizable, General Applied Topology, 2 (2003), 351-360.
- Del Prete, M. Di Iorio, Ľ. Holá, Uniform structures on hyperspaces and uniform topologies on spaces of multifunctions, Demonstratio Math. 36, (2003), 985-1000.
- C.Costantini, Ľ. Holá, P. Vitolo, Tightness, character and related properties of hyperspace topologies, Topology and its Applications 142 (2004), 245-292.
- Ľ. Holá, R.A. McCoy, Relations approximated by continuous functions, PAMS, 133, 2173-2182, 2005.
- S. Caterino, R. Ceppitelli, Ľ. Holá, Hausdorff metric convergence on partial maps, Bolletino U.M.I. (8) 9 (2006), 645-656.
- Ľ. Holá, R.A. McCoy, Cardinal invariants of the topology of uniform convergence on compact sets on the space of densely continuous forms, Rocky Mountain Journal 37, 2007, 229-246.
- Ľ. Holá, Spaces of densely continuous forms, Topology Proceedings 31 (2007), 1-6.
- Ľ. Holá, R.A. McCoy, J. Pelant, Approximations of relations by continuous functions, Topology and its Applications 154 (2007), 2241-2247.
- Ľ. Holá, R.A. McCoy, Relations approximated by continuous functions in the Vietoris topology, Fundamenta Mathematicae 195 (2007), 205-219.
- G. Artico, Ľ. Holá, U. Marconi, R. Moresco, Approximation by continuous functions in the Fell topology, Topology and its Applications 155 (2008), 2150-2157.
- P. Brandi, R. Ceppitelli, Ľ. Holá, Boundedly UC spaces and topologies on function spaces, Set-Valued Analysis 16 (2008), 357-373.
- S. Caterino, R. Ceppitelli, Ľ. Holá, L. Zampogni, Some topologies on the space of usco maps and densely continuous forms, Acta Mathematica Hungarica 121 (2008), 187-201.
- Ľ. Holá, T. Jain, R.A. McCoy, Topological properties of the multifunction space L(X) of cusco maps, Mathematica Slovaca 58 (2008), 763-780.
- Ľ. Holá, D. Holý, Minimal usco maps, densely continuous forms and upper semi-continuous functions, Rocky Mountain Journal of Mathematics 39 (2009), 545-562.
- Ľ. Holá, Z. Piotrowski, Set of continuity points of functions with values in generalized metric spaces, Tatra Mountains Mathematical Publications 39 (2009) 149-160.
- Ľ. Holá, L. Zsilinszky, Vietoris topology on partial maps with compact domains, Topology and its Applications 157 (2010), 1439-1447.
- A. Caserta, G. Di Maio, Ľ. Holá, Arzela‘s theorem and strong uniform convergence on bornologies, Journal of Mathematical Analysis and Applications 371 (2010), 384-392.
- A. Caserta, G. Di Maio, Ľ. Holá, (Strong) weak exhaustivness and (strong) uniform continuity, Filomat 24 (2010), 63-75.
- Ľ. Holá, D. Holý, Pointwise convergence of quasicontinuous mappings and Baire spaces, Rocky Mountain Journal of Mathematics 41 (2011), 1883-1894.
- J. Borsík, Ľ. Holá, D. Holý, Baire spaces and quasicontinuous mappings, Filomat 25 (2011), 69-83.
- Ľ. Holá, Complete metrizability of topologies of strong uniform convergence on bornologies, Journal of Mathematical Analysis and Applications 387 (2012), 770-775.
- Ľ. Holá, B. Novotný, Subcontinuity, Mathematica Slovaca 62 (2012), 345-362.
- Ľ. Holá, B. Novotný, On normality of the Wijsman topology, Annali di Matematica 192 (2012), 349-359.
- Ľ. Holá, D. Holý, Spaces of lower semicontinuous set-valued maps, Mathematica Slovaca 83 (2013), 863-870.
- Ľ. Holá, Functional characteriyations of p-spaces, Central European Journal of Mathematics 11 (2013) 2197-2202.
- A. Caterino, R. Ceppitelli, Ľ. Holá, Some generaliyations of Back s Theorem, Topology and its Applications 160 (2013) 2386-2395.
- Ľ. Holá, D. Holý, Relations between minimal usco and minimal cusco maps, Portugaliae Mathematica 70 (2013), 211-224.
- Ľ. Holá, B. Novotný, Cardinal functions, bornologies and function spaces, Annali di Mathematica 193 (2014), 1319-1327.
- Ľ. Holá, D. Holý, New characterizations of minimal cusco maps, Rocky Mountain Math. J. 44 (2014), 1851-1866.
- Ľ. Holá, B. Novotný, Topology of uniform convergence and Čech-Stone compactification, Journal of Mathematical Analysis and Applications, 424 (2015), 470-474.
- Ľ. Holá, A. Mirmostafaee, Z. Piotrowski, Points of openness and closedness of some mappings, Banach J. Math. Anal. 1 (2015) 243-252.
- Ľ. Holá, L. Zsilinszky, On generalized metric properties of the Fell hyperspace, Annali di Matematica 194 (2015), 1259-1267.
- Ľ. Holá, L. Zsilinszky, Completeness properties of the graph topology, Topology Proceedings 46 (2015), 1-14.
- Ľ. Holá, An embedding in the Fell topology, Topology and its Applications, 180 (2015), 161-166.