This substitution map that is more varied than JavaFan's quick-and-dirty solution, so by looking at the output you have a better idea what the original space was.

    use charnames ':full';
    %spaces = (
        "\N{CHARACTER TABULATION}" => "\N{SYMBOL FOR HORIZONTAL TABULA
+TION}",
        "\N{LINE FEED (LF)}" => "\N{SYMBOL FOR LINE FEED}",
        "\N{LINE TABULATION}" => "\N{SYMBOL FOR VERTICAL TABULATION}",
        "\N{FORM FEED (FF)}" => "\N{SYMBOL FOR FORM FEED}",
        "\N{CARRIAGE RETURN (CR)}" => "\N{SYMBOL FOR CARRIAGE RETURN}"
+,
        "\N{SPACE}" => "\N{SYMBOL FOR SPACE}",
        "\N{NEXT LINE (NEL)}" => "\N{DOWNWARDS ARROW WITH CORNER LEFTW
+ARDS}",
        "\N{NO-BREAK SPACE}" => "\N{MIDDLE DOT}",
        "\N{OGHAM SPACE MARK}" => "\N{HYPHEN-MINUS}",
        "\N{MONGOLIAN VOWEL SEPARATOR}" => "\N{HYPHEN-MINUS}",
        "\N{EN QUAD}" => "\N{EN DASH}",
        "\N{EM QUAD}" => "\N{EM DASH}",
        "\N{EN SPACE}" => "\N{EN DASH}",
        "\N{EM SPACE}" => "\N{EM DASH}",
        "\N{THREE-PER-EM SPACE}" => "\N{HYPHEN-MINUS}",
        "\N{FOUR-PER-EM SPACE}" => "\N{HYPHEN-MINUS}",
        "\N{SIX-PER-EM SPACE}" => "\N{HYPHEN-MINUS}",
        "\N{FIGURE SPACE}" => "\N{FIGURE DASH}",
        "\N{PUNCTUATION SPACE}" => "\N{MIDDLE DOT}",
        "\N{THIN SPACE}" => "\N{MIDDLE DOT}",
        "\N{HAIR SPACE}" => "\N{MIDDLE DOT}",
        "\N{LINE SEPARATOR}" => "\N{DOWNWARDS ARROW WITH CORNER LEFTWA
+RDS}",
        "\N{PARAGRAPH SEPARATOR}" => "\N{PILCROW SIGN}",
        "\N{NARROW NO-BREAK SPACE}" => "\N{MIDDLE DOT}",
        "\N{MEDIUM MATHEMATICAL SPACE}" => "\N{MIDDLE DOT}",
        "\N{IDEOGRAPHIC SPACE}" => "\N{IDEOGRAPHIC NUMBER ZERO}",
    );
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For accuracy, however, nothing beats the uniquote filter. The result does not look like in a text editor anymore, but solves the problem completely: all invisible characters (not only spaces) are quoted/made visible.