Journal of the Ramanujan Mathematical Society

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Spaces of Diversity One


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

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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.
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  • Spaces of Diversity One

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Authors

M. Rajagopalan
Department of Mathematics, Tennessee State University, Nashville, TN 37203, United States
S. P. Franklin
Institute of Intelligent Systems & Department For Mathematical Science Memphis State University Memphis, TN 38152, United States

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.