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A Positive Answer to Velichko's Question

Abstract We give positive answer to Velichko's question in which the quotient and 𝑠-map is replaced by a sequence-covering and 𝑐𝑠-map. In addition, let 𝑋 have a star-countable 𝑘-network, then 𝑋 is a sequence-covering and 𝑐𝑠-image of a locally separable metric space if and only if 𝑋 is a sequencecovering and 𝑐𝑠-image of a metric space.