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## Commentationes Mathematicae

2006 | 46 | 1 |
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### On $$\mathbb{I}$$-approximate limits and $$\mathbb{I}$$-approximate smoothness

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In this paper we present some results based on slightly modified idea of the $$\mathbb{I}$$-density introduced by Władysław Wilczyński. Some theorems are generalized versions of results from [2] and [3]. We investigate properties of functions from $$\mathbb{R}^X$$, where $$X$$ is supplied with the $$\mathbb{I}$$-density. We try to free our considerations from the assumption of Baire property, or measurability. In some cases this is not done yet. Star-marked statements still need that assumption, proofs presented here are done for Baire property, but it is possible to adapt them to measure. $$\mathbb{I}$$-density itself does not require any structure of considered space but a metric vector space over $$\mathbb{R}$$. However, in last section we confine ourselves to $$\mathbb{R}$$, for we make use of $$\mathbb{R}$$’s structure for simplicity. To find more about related topics see [4], [5], more bibliography one can find in [1] and [5].
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2006
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2017-12-19
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