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SOOCHOW JOURNAL OF MATHEMATICS

Volume 33, No. 4, pp. 771-786, October 2007




ON A TYPICAL TOPOLOGY INDUCED BY A GRILL


BY


B. ROY AND M. N. MUKHERJEE




Abstract. In the present paper, we define a kind of topology obtained as an associated structure on a topological space $ X$ induced by a grill on $ X$. Such a topology is studied in certain detail as to some of its basic properties. Then a sort of suitability condition of a grill with the underlying topology of the space $ X$ is formulated. After ample analysis and characterizations of such a suitability condition, the introduced topology is studied in conjunction with the given one (under assumption of the said condition) with regard to some topological properties.

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Received July 26, 2006; revised January 29, 2007.

AMS Subject Classification. 54A10, 54A99.

Key words. grill, topology suitable for grill, $ \sigma$-grill.

The author acknowledges the financial support from C.S.I.R., New Delhi, India.