J. K. KOHLI 1, D. SINGH 2 AND B. K. TYAGI 3 1. Department of Mathematics, Hindu College, University of Delhi, Delhi-110007, INDIA, e-mail: jk kohli@yahoo.co.in
2. Department of Mathematics, Sri Aurobindo College, University of Delhi, New Delhi-110017, INDIA, e-mail: dstopology@gmail.com
3. Department of Mathematics, A.R.S.D. College, University of Delhi, New Delhi-1100021, INDIA, e-mail: brijkishore.tygi@gmail.com
A new generalization of local connectedness called âR_cl-local connectednessâ is intro-duced. Basic properties of R_cl-locally connected spaces are studied and their place in the hierarchy of variants of local connectedness which already exist in the literature is discussed. R_cl-local connectedness is preserved in the passage to r_cl-open sets and is invariant under disjoint topological sums. A necessary and sufficient condition for a product of R_cl-local connected spaces be R_cl-locally connected proved. Preservation of R_cl-local connectedness under mappings is investigated. It is shown that R_cl-local con-nectedness is preserved under quotients and an r_cl-quotient of an R_cl-locally connected space is locally connected. The category of R_cl-locally connected spaces is properly con-tained in the category of sum connected spaces (Math. Nachrichten 82(1978), 121-129; Ann. Acad. Sci. Fenn. AI Math. 3 (1977), 185-205) and constitutes a mono-coreflective subcategory of TOP.
