Introduzione
Abstract
En
Given a topological space
and a subset
of
, the topology
is called the simple extension of
by
(see Levine 3).Here we show how to recognize when two subsets
and
of
define the same simple extension of
and we give a characterization of those expansions of
which are simple extensions of
by suitable subsets of
.
Given a topological space
![(S,\tau)](https://358864.dpsou.asia/plugins/generic/latexRender/cache/24d0af7da8fd756d99494d7024bbe278.png)
![X](https://358864.dpsou.asia/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![S](https://358864.dpsou.asia/plugins/generic/latexRender/cache/5dbc98dcc983a70728bd082d1a47546e.png)
![\tau(x) = ≤ft{A \cup (A' ∩ X)/A,A' ∈ τ \right}](https://358864.dpsou.asia/plugins/generic/latexRender/cache/a81afcaecde491debecd90591ca286ef.png)
![\tau](https://358864.dpsou.asia/plugins/generic/latexRender/cache/a6f317b268ae825d94f832f970af607c.png)
![X](https://358864.dpsou.asia/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![X](https://358864.dpsou.asia/plugins/generic/latexRender/cache/02129bb861061d1a052c592e2dc6b383.png)
![Y](https://358864.dpsou.asia/plugins/generic/latexRender/cache/57cec4137b614c87cb4e24a3d003a3e0.png)
![S](https://358864.dpsou.asia/plugins/generic/latexRender/cache/5dbc98dcc983a70728bd082d1a47546e.png)
![\tau](https://358864.dpsou.asia/plugins/generic/latexRender/cache/a6f317b268ae825d94f832f970af607c.png)
![\tau](https://358864.dpsou.asia/plugins/generic/latexRender/cache/a6f317b268ae825d94f832f970af607c.png)
![\tau](https://358864.dpsou.asia/plugins/generic/latexRender/cache/a6f317b268ae825d94f832f970af607c.png)
![S](https://358864.dpsou.asia/plugins/generic/latexRender/cache/5dbc98dcc983a70728bd082d1a47546e.png)
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