Abstract
The aim of this paper is to show the admissibility and the AR-property of some unbounded convex sets in a class of non-locally convex linear metric spaces.
Similar content being viewed by others
References
Bessaga, C., Dobrowolski, T.: Some open problems in the border of functional analysis and topology. In: Proc. Int. Conf. Geom. Topol., Warsaw (1978)
Bessaga, C., Pelczynski, A.: Selected Topics in Infinite-Dimensional Topology. Polish Sci., Warszawa (1975)
Dobrowolski, T.: On extending mappings into nonlocally convex linear metric spaces. Proc. Am. Math. Soc. 93, 555–560 (1985)
Granas, A., Dugundji, J.: Fixed Point Theory. Springer, Berlin (2003)
Klee, V.: Shrinkable neighborhoods in Hausdorff linear spaces. Math. Ann. 141, 281–285 (1960)
Klee, V.: Leray-Schauder theory without local convexity. Math. Ann. 141, 286–296 (1960)
Nhu, N.T., Tri, L.H.: No Roberts space is a counter-example to Schauder’s conjecture. Topology 33, 371–378 (1994)
Nhu, N.T., Tri, L.H.: Every needle point space contains a compact convex AR-set with no extreme point. Proc. Am. Math. Soc. 120, 1261–1265 (1994)
Thanh, N.H.: The fixed point property of the Cartesian product of Roberts spaces. Fixed Point Theory 13, 267–272 (2012)
Tri, L.H., Thanh, N.H.: Some remarks on the AR-problem. Acta Math. Vietnam. 34, 389–400 (2009)
West, J.E.: Problems in infinite-dimensional topology. In: van Mill, J., Reed, G.M. (eds.) Open Problems in Topology. North-Holland, Amsterdam (1990)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Thanh, N.H. The Admissibility and the AR-Property of Some Unbounded Convex Sets in a Class of Non-locally Convex Spaces Containing l p (0<p<1). Vietnam. J. Math. 42, 191–203 (2014). https://doi.org/10.1007/s10013-014-0059-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10013-014-0059-1