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  • Author or Editor: J. Ewert x
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The almost uniform convergence is between uniform and quasi-uniform one. We give some necessary and sufficient conditions under which the almost uniform convergence coincides on compact sets with uniform, quasi-uniform or uniform convergence, respectively. In the second section continuity of almost uniform limits is considered. Finally we characterize the set of all points at which a net of functions is almost uniformly convergent to a given function.

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If X is a topological space and (Y,d) is a metric space, then for each locally bounded function f : XY all possible superpositions of oscillations and quasi-oscillations give at most eight functions.

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In this paper we consider the structure of l in the modular sequence space T(A, {f n}) defined in [2]. We obtain the conditions when l = T(A, {f n}). We prove that if l T(A, {f n}), then the space l is an F σ, σ-strorigly porous set in T(A, {f n}).

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