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Context: a touchscreen monitor in which the user can choose which business lines or activities can be displayed in a State.
After selecting some of the filters in the box on the left, the user touches the button "Apply Filters".
The filter's box will close automatically, the map changes and the boxes on the right (which summarize the filtering situation) appear on the right of the screen.
How can I keep the large amount of selected filters still visible when the filter's panel is closed?
Depending on the amount of filters available and selected you could collapse the filter panel to only show the selected filters in a vertical list with the ability to remove the filter. Alternatively you could show the filters in an overlay in that spot on collapse. You could consider not showing them since the user knows where the filters are and can quickly, presumably, access them. You also have the entire rest of the screen presumably to place them unobtrusively. You could also place them in or in proximity to the panel on the right since that is the result of those filters.
I believe where you want to show them will depend on your design. You can show them in quite different places, but I thin the question here is: Do you want your filters to be visible, or can you have them a click/touch away? If they need to be visible, user47794's answer covers the main possibilities, any of them is good.
You should definitely make it visible that there are filters, but perhaps you don't need to show their names. I can imagine for example that if the user will only apply filters once and then continue using the app for a very long time without modifying them, you can probably do without the names. In that case, you wouldn't show the names, but you'd show:
"There are 7 filters currently applied."
And then have the user click or touch to expand and see their names. Advantage: You need less space than if you have to display everything.
