diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index 221191773186e..fa0eaa5c05279 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1594,7 +1594,8 @@ def to_numpy(
 
     def map(self, mapper, na_action: Literal["ignore"] | None = None):
         if is_numeric_dtype(self.dtype):
-            return map_array(self.to_numpy(), mapper, na_action=na_action)
+            result = map_array(self.to_numpy(), mapper, na_action=na_action)
+            return self._cast_pointwise_result(result)
         else:
             return super().map(mapper, na_action)
 
diff --git a/pandas/core/arrays/base.py b/pandas/core/arrays/base.py
index 1cd10a9eef9d1..1c5e7881c215c 100644
--- a/pandas/core/arrays/base.py
+++ b/pandas/core/arrays/base.py
@@ -2530,7 +2530,8 @@ def map(self, mapper, na_action: Literal["ignore"] | None = None):
             If the function returns a tuple with more than one element
             a MultiIndex will be returned.
         """
-        return map_array(self, mapper, na_action=na_action)
+        results = map_array(self, mapper, na_action=na_action)
+        return self._cast_pointwise_result(results)
 
     # ------------------------------------------------------------------------
     # GroupBy Methods
diff --git a/pandas/core/arrays/masked.py b/pandas/core/arrays/masked.py
index 0402452e484ea..e56ca7b0fed39 100644
--- a/pandas/core/arrays/masked.py
+++ b/pandas/core/arrays/masked.py
@@ -1395,7 +1395,8 @@ def max(self, *, skipna: bool = True, axis: AxisInt | None = 0, **kwargs):
         return self._wrap_reduction_result("max", result, skipna=skipna, axis=axis)
 
     def map(self, mapper, na_action: Literal["ignore"] | None = None):
-        return map_array(self.to_numpy(), mapper, na_action=na_action)
+        result = map_array(self.to_numpy(), mapper, na_action=na_action)
+        return self._cast_pointwise_result(result)
 
     @overload
     def any(