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September 10, 2016 / porton

An error in my math book corrected

After noticing an error in my math book, I rewritten its section “Funcoids and filters” to reflect that (\mathsf{RLD})_\Gamma = (\mathsf{RLD})_{\mathrm{in}}.

Previously I proved an example demonstrating that (\mathsf{RLD})_\Gamma \ne (\mathsf{RLD})_{\mathrm{in}}, but this example is believed by me to be wrong. The example was removed from the book.

Thus I removed all references to (\mathsf{RLD})_\Gamma (as it is the same as (\mathsf{RLD})_{\mathrm{in}}) and reworked the chapter “Funcoids and filters” to reflect the change.

The book is available free of change at this Web page.

The story of the past:

(\mathsf{RLD})_\Gamma was defined by the formula (\mathsf{RLD})_\Gamma f = \bigsqcap^{\mathsf{RLD}} \mathrm{up}^\Gamma\, f.

From the theorem in “The diagram” section (the theorem with a diagram) it trivially follows that (\mathsf{RLD})_\Gamma f = (\mathsf{RLD})_{\mathrm{in}} f. It follows trivially, but I have found this only today.


One Comment

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  1. porton / Sep 10 2016 20:10

    I’ve added to the post a note with my old definition.

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