Concerning semi-quotient mappings
Main Article Content
Abstract
Abstract. In 1989, N.V. Velichko [1] introduced a semi-quotient ws-mapping, and proved that a sequential space has a point-countable k-network if and only if it is a semi-quotient ws-image of a metric space. Recently, Shou Lin and Jinjin Li [2] introduced and studied the concept of wks-mappings, wcs-mappings, and proved that every sequential space with a point-countable k-network is preserved by a continuous closed mapping. In this article, we introduce a class of mappings named wscc-mappings and give some properties of semi-quotient wscc-mappings. Moreover, we also give a result stating that every sequential space with a point-countable k-network is preserved by a continuous closed compact mapping.
Keywords: semi-quotient ws-mappings; wks-mappings; wcs-mappings; wscc-mappings; semi-quotient wscc-mappings
References
[2] Shou Lin, Generalized Metric Spaces and Mappings, Second Edition, Beijing: Science Press, 2007 (in Chinese).
[3] G. Gruenhage, E. Michael, and Y. Tanaka, Spaces determined by point- countable covers, Pacific J. Math., 113, (1984), 303-332.
[4] Shou Lin, Jinjin Li, Semi-quotient mappings and spaces with compact-countable k-networks, Advances in Mathematics(China), 38(4), (2009), 417-426.
[5] R. Engelking, General Topology, Berlin: Heldermann, (1989).
[6] N. Levine, A decomposition of continuity in topological spaces, Amer. Math. Monthly, 68, (1961), 44-46.