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Rδ-supercontinuous functions

Kohli J. K., Tyagi B. K., Singh D., Aggarwal J.

Demonstratio Mathematica

2014

Vol. 47, nr 2

433--448

A new class of functions called ‘Rδ-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity which already exist in the literature is elaborated. The class of Rδ-supercontinuous functions (Math. Bohem., to appear) properly contains the class of Rz-supercontinuous functions which in its turn properly contains the class of Rcl-supercontinuous functions (Demonstratio Math. 46(1) (2013), 229–244) and so includes all cl-supercontinuous (=clopen continuous) functions (Applied Gen. Topol. 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).

Rcl-supercontinuous functions

Tyagi B. K., Kohli J. K., Singh D.

Demonstratio Mathematica

2013

Vol. 46, nr 1

229--244

A new class of functions called ‘Rcl-supercontinuous functions’ is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity that already exist in the literature is elaborated. The class of Rcl-supercontinuous functions properly contains the class of cl-supercontinuous (≡ clopen continuous) functions (Applied Gen. Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772) and is strictly contained in the class of Rδ-supercontinuous functions which in its turn, is properly contained in the class of R-supercontinuous functions (Demonstratio Math. 43(3) (2010), 703–723).

Between local connectedness and sum connectedness

Kohli J. K., Singh D., Tyagi B. K.

Commentationes Mathematicae

2013

Vol 53, No. 1

3--16

A new generalization of local connectedness called Z-local connectedness is introduced. Basic properties of Z-locally connected spaces are studied and their place in the hierarchy of variants of local connectedness, which already exist in the literature, is elaborated. The class of Z-locally connected spaces lies strictly between the classes of pseudo locally connected spaces (Commentations Math. 50(2)(2010),183-199) and sum connected spaces ( weakly locally connected spaces) (Math. Nachrichten 82(1978), 121-129; Ann. Acad. Sci. Fenn. AI Math. 3(1977), 185- 205) and so contains all quasi locally connected spaces which in their turn contain all almost locally connected spaces introduced by Mancuso (J. Austral. Math. Soc. 31(1981), 421-428). Formulations of product and subspace theorems for Z-locally connected spaces are suggested. Their preservation under mappings and their interplay with mappings are discussed. Change of topology of a Z-locally connected space is considered so that it is simply a locally connected space in the coarser topology. It turns out that the full subcategory of Z-locally connected spaces provides another example of a mono-coreflective subcategory of TOP which properly contains all almost locally connected spaces.