Article
Full entry |
PDF
(0.1 MB)
Feedback
PDF
(0.1 MB)
Feedback
Keywords:
connected; Cantor-connected; metric space; topological space; approach space
connected; Cantor-connected; metric space; topological space; approach space
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.
References:
[1] Arhangel'skii A., Wiegandt R.: Connectedness and disconnectedness in topology. Gen. Topology Appl. 5 (1975), 9-33. MR 0367920
[2] Banas J., Goebel K.: Measures of Non-Compactness in Banach Spaces. Marcel Dekker, 1980. MR 0591679
[3] Cantor G.: Über unendliche, lineare punktmannigfaltigkeiten. Math. Ann. 21 (1883), 545-591. MR 1510215
[4] Connell E.M.: Properties of fixed point spaces. Proc. Amer. Math. Soc. 10 (1959), 974-979. MR 0110093 | Zbl 0163.17705
[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 0034573 | Zbl 0036.13001
[7] Herrlich H.: Categorical topology 1971-1981. Gen. Topol. Rel. Mod. Analysis and Algebra, Proc. 5th Prague Top. Symp., pages 279-383, 1983. MR 0698425 | Zbl 0502.54001
[8] Herrlich H.: Einführung in die Topologie. Heldermann Verlag, 1986. MR 0846211 | Zbl 0628.54001
[9] Isiwata T.: Metrization of additive $\kappa $-metric spaces. Proc. Amer. Math. Soc. 100 (1987), 164-168. MR 0883422 | Zbl 0612.54033
[10] Klee V.L.: Stability of the fixed point property. Colloq. Math. 8 (1961), 43-46. MR 0126261 | Zbl 0101.15101
[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 1029625 | Zbl 0706.18002
[13] Lowen R.: Kuratowski's measure of non-compactness revisited. Quarterly J. Math. Oxford 39 (1988), 235-254. MR 0947504 | Zbl 0672.54025
[14] Lowen R.: Approach spaces : a common supercategory of TOP and MET. Math. Nachr. 141 (1989), 183-226. MR 1014427 | Zbl 0676.54012
[15] Lowen R.: A topological category suited for approximation theory. J. Approximation Theory 56 (1989), 108-117. MR 0977878 | Zbl 0675.41046
[16] Marny T.: On epireflective subcategories of topological categories. Gen. Topol. Appl. 10 (1979), 175-181. MR 0527843 | Zbl 0415.54007
[17] Mrowka S., Pervin W.J.: On uniform connectedness. Proc. Amer. Math. Soc. 15 (1964), 446-449. MR 0161307 | Zbl 0126.18301
[18] Preuss G.: E-zusammenhangende Raüme. Manuscripta Math. 3 (1970), 331-342. MR 0282323
[19] Preuss G.: Relative connectedness and disconnectedness in topological categories. Quaest. Math. 2 (1977), 297-306. MR 0500841
[20] Preuss G.: Connection properties in topological categories and related topics. Lecture Notes in Mathematics 719 (1979), 293-307. MR 0544654 | Zbl 0411.18002
[21] Sčepin E.V.: On $\kappa $-metrizable spaces. Math. USSR Izv. 14 (1980), 407-440.
Search
Partner of
