Locally dδ -connected and locally Dδ -compact spaces

Locally dδ -connected and locally Dδ -compact spaces

The local analogues of the notions of dδ -connectedness and Dδ -compactness of a topological space areintroduced, and are named respectively, locally dδ -connectedness and locally Dδ -compactness. Several propertiesincluding characterization of the concepts are discussed.

___

  • [1] Bourbaki N. Elements of Mathematics, General topology Part 1. Paris, France: Hermann, 1966.
  • [2] Hocking JG, Young GS. Topology. London, UK: Addison-Wesley Publishing Co., Inc., 1961.
  • [3] Kohli JK, Singh D. Dδ -supercontinuous functions. Indian Journal of Pure and Applied Mathematics 2003; 34 (7): 1089-1100.
  • [4] Kohli JK, Singh D. Between compactness and quasicompactness. Acta Mathematica Hungarica 2005; 106 (4): 317-329.
  • [5] Kohli JK, Singh D. Between regularity and complete regularity and a factorization of complete regularity. Studii şi Cercetări Ştiinţifice. Seria: Matematică. Universitatea din Bacău 2007; 17: 125-134.
  • [6] Singh TB. Elements of topology. Boca Raton, FL, USA: CRC Press, 2013.
  • [7] Singh D. Pseudo strongly θ -continuous functions. Scientific Studies and Research. Series Mathematics and Informatics 2013; 23 (2): 127-140.
  • [8] Singh D, Mathur H. Generalizations of connected and compact sets by dδ -closure operator. Bulletin of the Belgian Mathematical Society. Simon Stevin 2019; 26 (2): 255-273.