BUG: Parameter col_space of to_html method not working with multi-level columns

pandas/io/formats/html.py

@@ -68,10 +68,16 @@ def __init__(
         self.table_id = table_id
         self.render_links = render_links
 
-        self.col_space = {
-            column: f"{value}px" if isinstance(value, int) else value
-            for column, value in self.fmt.col_space.items()
-        }
+        self.col_space = {}
+        for column, value in self.fmt.col_space.items():
+            col_space_value = f"{value}px" if isinstance(value, int) else value
+            # GH 53885: Handling case where column is MultiIndex
+            # Flatten the data in the multi index and add in the map
+            if isinstance(column, tuple):
+                for column_index in column:
+                    self.col_space[str(column_index)] = col_space_value
+            else:
+                self.col_space[column] = col_space_value
 
     def to_string(self) -> str:
         lines = self.render()

pandas/tests/io/formats/data/html/gh53885_expected_output.html

@@ -0,0 +1,26 @@
+<table border="1" class="dataframe">
+  <thead>
+    <tr>
+      <th style="min-width: 100px;"></th>
+      <th style="min-width: 100px;">1</th>
+      <th style="min-width: 100px;">2</th>
+    </tr>
+    <tr>
+      <th style="min-width: 100px;"></th>
+      <th style="min-width: 100px;">1</th>
+      <th style="min-width: 100px;">1</th>
+    </tr>
+  </thead>
+  <tbody>
+    <tr>
+      <th>0</th>
+      <td>1</td>
+      <td>2</td>
+    </tr>
+    <tr>
+      <th>1</th>
+      <td>3</td>
+      <td>4</td>
+    </tr>
+  </tbody>
+</table>

pandas/tests/io/formats/test_to_html.py

@@ -896,3 +896,12 @@ def test_to_html_float_format_object_col(datapath):
     result = df.to_html(float_format=lambda x: f"{x:,.0f}")
     expected = expected_html(datapath, "gh40024_expected_output")
     assert result == expected
+
+
+def test_to_html_multiindex_col_with_colspace(datapath):
+    # GH#53885
+    df = DataFrame([[1, 2], [3, 4]])
+    df.columns = MultiIndex.from_tuples([(1, 1), (2, 1)])
+    result = df.to_html(col_space=100)
+    expected = expected_html(datapath, "gh53885_expected_output")
+    assert result == expected