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.


D. Zhao, A compactness type of topological property, Questiones Mathemeticae 28, (2005), 1–11.


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.


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.


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.


H. J. K. Junnila, Neighbornets, Pacific J. Math. 76, no. 1 (1978), 83–108.


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.


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Universitat Politècnica de València

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