Between local connectedness and sum connectedness

• Autorzy: Kohli J. K. , Singh D. , Tyagi B. K.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Z-locally connected space; almost locally connected space; quasi locally connected space; pseudo locally connected space; sum connected space; regular open set; regular F[sigma]-set; theta-open set; cl-supercontinuous function; mono-coreflective subcategory

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol 53, No. 1
• Strony: 3--16
• Opis fizyczny: Bibliogr. 38 poz.

Twórcy

autor

Kohli J. K.

• Department of Mathematics, Hindu College, University of Delhi, Delhi-110007, India

autor

Singh D.

• Department of Mathematics, Sri Aurobindo College, University of Delhi, Delhi-110017, India

autor

Tyagi B. K.

• Department of Mathematics, A. R. S. D. College, University of Delhi, Delhi-110021, India

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