Journal of the Ramanujan Mathematical Society

M. Rajagopalan

Abstract

Prof. M. Venkataraman passed away on the 18th, November 1990 at 5.15 p.m. when he was only 67. The immediate cause of his death is possibly cerebral hemorrhage according to some doctors in the nursing home attached to the Aurobindo Ashram in Pondicherry where he died.

Full Text

     

A. Blaszczyk ¹, M. Rajagopalan ², A. Szymanski ³

Affiliations
1 Silesian University, Bankowa 14. 40-007 Katowice, PL
2 Tennessee State University, Nashville, TN 37209, US
3 Slippery Rock University, Slippery Rock, PA 16057, US

Abstract

It is easy to observe that extremelly disconnected spaces may contain subspaces which are not extremally disconnected. Discrete spaces contain only extremally disconnected subspaces. i.e., they are instances of hereditarily extremally disconnected spaces. We show that there are many other examples of such spaces. We discuss their topological properties and groups of homeomorphisms.

Keywords

Extremally Disconnected, Subspace, Almost Disjoint.

Full Text

     

M. Rajagopalan ¹, S. P. Franklin ²

Affiliations
1 Department of Mathematics, Tennessee State University, Nashville, TN 37203, US
2 Institute of Intelligent Systems & Department For Mathematical Science Memphis State University Memphis, TN 38152, US

Abstract

Spaces in which every non-empty open set is homeomorphic to the whole space (called divine spaces) are exhibited and their elementary properties explored. Several families of such spaces are constructed, including metrizable and ordered divine spaces of all infinite cardinalities. These are all constructed via the method of condensation. Many questions are raised.

Keywords

Divine Spaces, Method of Condensation.

Full Text