A new cardinal function on topological spaces


  • Dewi Kartika Sari Nanyang Technological University ; Universitas GadjahMada
  • Dongsheng Zhao Nanyang Technological University




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


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.


Download data is not yet available.

Author Biographies

Dewi Kartika Sari, Nanyang Technological University ; Universitas GadjahMada

Mathematics and Mathematics Education, National Institute of Education

Dongsheng Zhao, Nanyang Technological University

Mathematics and Mathematics Education, National Institute of Education


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




How to Cite

D. K. Sari and D. Zhao, “A new cardinal function on topological spaces”, Appl. Gen. Topol., vol. 18, no. 1, pp. 75–90, Apr. 2017.



Regular Articles