Previous |  Up |  Next

Article

Title: Cantor-connectedness revisited (English)
Author: Lowen, R.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 33
Issue: 3
Year: 1992
Pages: 525-532
.
Category: math
.
Summary: Following Preuss' general connectedness theory in topological categories, a connectedness concept for approach spaces is introduced, which unifies topological connectedness in the setting of topological spaces, and Cantor-connectedness in the setting of metric spaces. (English)
Keyword: connected
Keyword: Cantor-connected
Keyword: metric space
Keyword: topological space
Keyword: approach space
MSC: 54A05
MSC: 54B30
MSC: 54D05
idZBL: Zbl 0782.54010
idMR: MR1209293
.
Date available: 2009-01-08T17:57:45Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118519
.
Reference: [1] Arhangel'skii A., Wiegandt R.: Connectedness and disconnectedness in topology.Gen. Topology Appl. 5 (1975), 9-33. MR 0367920
Reference: [2] Banas J., Goebel K.: Measures of Non-Compactness in Banach Spaces.Marcel Dekker, 1980. MR 0591679
Reference: [3] Cantor G.: Über unendliche, lineare punktmannigfaltigkeiten.Math. Ann. 21 (1883), 545-591. MR 1510215
Reference: [4] Connell E.M.: Properties of fixed point spaces.Proc. Amer. Math. Soc. 10 (1959), 974-979. Zbl 0163.17705, MR 0110093
Reference: [5] De Groot J., De Vries J., Van der Walt M.: Almost fixed point theorems for the euclidean plane.Math. Centre Tracts 1 (1967).
Reference: [6] Fort M.K.: Essential and non-essential fixed points.Amer. J. Math. 72 (1950), 315-322. Zbl 0036.13001, MR 0034573
Reference: [7] Herrlich H.: Categorical topology 1971-1981.Gen. Topol. Rel. Mod. Analysis and Algebra, Proc. 5th Prague Top. Symp., pages 279-383, 1983. Zbl 0502.54001, MR 0698425
Reference: [8] Herrlich H.: Einführung in die Topologie.Heldermann Verlag, 1986. Zbl 0628.54001, MR 0846211
Reference: [9] Isiwata T.: Metrization of additive $\kappa $-metric spaces.Proc. Amer. Math. Soc. 100 (1987), 164-168. Zbl 0612.54033, MR 0883422
Reference: [10] Klee V.L.: Stability of the fixed point property.Colloq. Math. 8 (1961), 43-46. Zbl 0101.15101, MR 0126261
Reference: [11] Kuratowski C.: Sur les espaces complets.Fund. Math. 15 (1930), 301-309.
Reference: [12] Lowen E., Lowen R.: Quasitopos hulls of categories containing topological and metric objects.Cahiers Topol. Géom. Diff. 30 (1989), 213-228. Zbl 0706.18002, MR 1029625
Reference: [13] Lowen R.: Kuratowski's measure of non-compactness revisited.Quarterly J. Math. Oxford 39 (1988), 235-254. Zbl 0672.54025, MR 0947504
Reference: [14] Lowen R.: Approach spaces : a common supercategory of TOP and MET.Math. Nachr. 141 (1989), 183-226. Zbl 0676.54012, MR 1014427
Reference: [15] Lowen R.: A topological category suited for approximation theory.J. Approximation Theory 56 (1989), 108-117. Zbl 0675.41046, MR 0977878
Reference: [16] Marny T.: On epireflective subcategories of topological categories.Gen. Topol. Appl. 10 (1979), 175-181. Zbl 0415.54007, MR 0527843
Reference: [17] Mrowka S., Pervin W.J.: On uniform connectedness.Proc. Amer. Math. Soc. 15 (1964), 446-449. Zbl 0126.18301, MR 0161307
Reference: [18] Preuss G.: E-zusammenhangende Raüme.Manuscripta Math. 3 (1970), 331-342. MR 0282323
Reference: [19] Preuss G.: Relative connectedness and disconnectedness in topological categories.Quaest. Math. 2 (1977), 297-306. MR 0500841
Reference: [20] Preuss G.: Connection properties in topological categories and related topics.Lecture Notes in Mathematics 719 (1979), 293-307. Zbl 0411.18002, MR 0544654
Reference: [21] Sčepin E.V.: On $\kappa $-metrizable spaces.Math. USSR Izv. 14 (1980), 407-440.
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_33-1992-3_14.pdf 199.0Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo