Cantor-connectedness revisited
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 525-532 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 54A05, 54B30, 54D05
Keywords: connected; Cantor-connected; metric space; topological space; approach space
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Lowen, R. Cantor-connectedness revisited. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 525-532. http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a13/

[1] Arhangel'skii A., Wiegandt R.: Connectedness and disconnectedness in topology. Gen. Topology Appl. 5 (1975), 9-33. | MR

[2] Banas J., Goebel K.: Measures of Non-Compactness in Banach Spaces. Marcel Dekker, 1980. | MR

[3] Cantor G.: Über unendliche, lineare punktmannigfaltigkeiten. Math. Ann. 21 (1883), 545-591. | MR

[4] Connell E.M.: Properties of fixed point spaces. Proc. Amer. Math. Soc. 10 (1959), 974-979. | MR | Zbl

[5] De Groot J., De Vries J., Van der Walt M.: Almost fixed point theorems for the euclidean plane. Math. Centre Tracts 1 (1967).

[6] Fort M.K.: Essential and non-essential fixed points. Amer. J. Math. 72 (1950), 315-322. | MR | Zbl

[7] Herrlich H.: Categorical topology 1971-1981. Gen. Topol. Rel. Mod. Analysis and Algebra, Proc. 5th Prague Top. Symp., pages 279-383, 1983. | MR | Zbl

[8] Herrlich H.: Einführung in die Topologie. Heldermann Verlag, 1986. | MR | Zbl

[9] Isiwata T.: Metrization of additive $\kappa $-metric spaces. Proc. Amer. Math. Soc. 100 (1987), 164-168. | MR | Zbl

[10] Klee V.L.: Stability of the fixed point property. Colloq. Math. 8 (1961), 43-46. | MR | Zbl

[11] Kuratowski C.: Sur les espaces complets. Fund. Math. 15 (1930), 301-309.

[12] Lowen E., Lowen R.: Quasitopos hulls of categories containing topological and metric objects. Cahiers Topol. Géom. Diff. 30 (1989), 213-228. | MR | Zbl

[13] Lowen R.: Kuratowski's measure of non-compactness revisited. Quarterly J. Math. Oxford 39 (1988), 235-254. | MR | Zbl

[14] Lowen R.: Approach spaces : a common supercategory of TOP and MET. Math. Nachr. 141 (1989), 183-226. | MR | Zbl

[15] Lowen R.: A topological category suited for approximation theory. J. Approximation Theory 56 (1989), 108-117. | MR | Zbl

[16] Marny T.: On epireflective subcategories of topological categories. Gen. Topol. Appl. 10 (1979), 175-181. | MR | Zbl

[17] Mrowka S., Pervin W.J.: On uniform connectedness. Proc. Amer. Math. Soc. 15 (1964), 446-449. | MR | Zbl

[18] Preuss G.: E-zusammenhangende Raüme. Manuscripta Math. 3 (1970), 331-342. | MR

[19] Preuss G.: Relative connectedness and disconnectedness in topological categories. Quaest. Math. 2 (1977), 297-306. | MR

[20] Preuss G.: Connection properties in topological categories and related topics. Lecture Notes in Mathematics 719 (1979), 293-307. | MR | Zbl

[21] Sčepin E.V.: On $\kappa $-metrizable spaces. Math. USSR Izv. 14 (1980), 407-440.