Let X be a Baire space, Y a topological space, Z a regular space and f:X times Y to Z be a horizontally quasi-continuous function. We will show that if $Y$ is first countable and f is quasi-continuous with respect to the first variable, then every horizontally quasi-continuous function :X times Y to Z is jointly quasi-continuous. This will extend Martin s Theorem of quasi-continuity of separately quasi-continuous functions for non-metrizable range. Moreover, we will prove quasi-continuity of f for the case Y is not necessarily first countable.

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