Cantor-connectedness revisited
Lowen, Robert
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 525-532 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

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.

Publié le : 1992-01-01
Classification:  54A05,  54B30,  54D05 
@article{118519,
     author = {Robert Lowen},
     title = {Cantor-connectedness revisited},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {525-532},
     zbl = {0782.54010},
     mrnumber = {1209293},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118519}
}

Lowen, Robert. Cantor-connectedness revisited. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 525-532. http://gdmltest.u-ga.fr/item/118519/

Arhangel'Skii A.; Wiegandt R. Connectedness and disconnectedness in topology, Gen. Topology Appl. 5 (1975), 9-33. (1975) | MR 0367920

Banas J.; Goebel K. Measures of Non-Compactness in Banach Spaces, Marcel Dekker, 1980. | MR 0591679

Cantor G. Über unendliche, lineare punktmannigfaltigkeiten, Math. Ann. 21 (1883), 545-591. (1883) | MR 1510215

Connell E.M. Properties of fixed point spaces, Proc. Amer. Math. Soc. 10 (1959), 974-979. (1959) | MR 0110093 | Zbl 0163.17705

De Groot J.; De Vries J.; Van Der Walt M. Almost fixed point theorems for the euclidean plane, Math. Centre Tracts 1 (1967). (1967)

Fort M.K. Essential and non-essential fixed points, Amer. J. Math. 72 (1950), 315-322. (1950) | MR 0034573 | Zbl 0036.13001

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

Herrlich H. Einführung in die Topologie, Heldermann Verlag, 1986. | MR 0846211 | Zbl 0628.54001

Isiwata T. Metrization of additive $\kappa $-metric spaces, Proc. Amer. Math. Soc. 100 (1987), 164-168. (1987) | MR 0883422 | Zbl 0612.54033

Klee V.L. Stability of the fixed point property, Colloq. Math. 8 (1961), 43-46. (1961) | MR 0126261 | Zbl 0101.15101

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

Lowen E.; Lowen R. Quasitopos hulls of categories containing topological and metric objects, Cahiers Topol. Géom. Diff. 30 (1989), 213-228. (1989) | MR 1029625 | Zbl 0706.18002

Lowen R. Kuratowski's measure of non-compactness revisited, Quarterly J. Math. Oxford 39 (1988), 235-254. (1988) | MR 0947504 | Zbl 0672.54025

Lowen R. Approach spaces : a common supercategory of TOP and MET, Math. Nachr. 141 (1989), 183-226. (1989) | MR 1014427 | Zbl 0676.54012

Lowen R. A topological category suited for approximation theory, J. Approximation Theory 56 (1989), 108-117. (1989) | MR 0977878 | Zbl 0675.41046

Marny T. On epireflective subcategories of topological categories, Gen. Topol. Appl. 10 (1979), 175-181. (1979) | MR 0527843 | Zbl 0415.54007

Mrowka S.; Pervin W.J. On uniform connectedness, Proc. Amer. Math. Soc. 15 (1964), 446-449. (1964) | MR 0161307 | Zbl 0126.18301

Preuss G. E-zusammenhangende Raüme, Manuscripta Math. 3 (1970), 331-342. (1970) | MR 0282323

Preuss G. Relative connectedness and disconnectedness in topological categories, Quaest. Math. 2 (1977), 297-306. (1977) | MR 0500841

Preuss G. Connection properties in topological categories and related topics, Lecture Notes in Mathematics 719 (1979), 293-307. (1979) | MR 0544654 | Zbl 0411.18002

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