A new cardinal function on topological spaces

Dewi Kartika Sari, Dongsheng Zhao


Using neighbourhood assignments, we introduce and study a new cardinal function, namely GCI(X), for every topological space X. We shall mainly investigate the spaces X with finite GCI(X). Some properties of this cardinal in connection with special types of mappings are also proved.


Neighbourhood assignments; Gauge compact space; gauge compact index; M-uniformly continuous mapping

Subject classification

54A25; 54C08; 54D30

Full Text:



A. Bouziad, The point of continuity property, neighbourhood assignments and filter convergences, Fund. Math. 218, no. 3 (2012), 225–242. https://doi.org/10.4064/fm218-3-2

D. Zhao, A compactness type of topological property, Questiones Mathemeticae 28, (2005), 1–11. https://doi.org/10.2989/16073600509486140

E. K. Van Douwen and W. F. Pfeffer, Some properties of the Sorgenfrey line and related spaces, Pacific J. Math. 81, no. 2 (1979), 371–377. https://doi.org/10.2140/pjm.1979.81.371

G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous lattices and domains, Vol. 93, Cambridge University Press, 2003. https://doi.org/10.1017/CBO9780511542725

G. Gruenhage, A survey of D-spaces, in: Set Theory and its Applications (L. Babinkostova, A. Caicedo, S. Geschke, M. Scheepers, eds.), Contemporary Mathematics, Vol. 533, 2011, pp. 13–28. https://doi.org/10.1090/conm/533/10502

H. J. K. Junnila, Neighbornets, Pacific J. Math. 76, no. 1 (1978), 83–108. https://doi.org/10.2140/pjm.1978.76.83

J. Dugundji, Topology, Allyn and Bacon, Inc., Boston, 1966.

J. Goubault-Larrecq, Non-Hausdorff topology and Domain Theory: Selected Topics in Point-Set Topology, Vol. 22, Cambridge University Press, 2013. https://doi.org/10.1017/CBO9781139524438

Abstract Views

Metrics Loading ...

Metrics powered by PLOS ALM

Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt