diff --git a/src/frequenz/channels/util/_select.py b/src/frequenz/channels/util/_select.py
index 80c09d61..1349791d 100644
--- a/src/frequenz/channels/util/_select.py
+++ b/src/frequenz/channels/util/_select.py
@@ -11,7 +11,7 @@
 import asyncio as _asyncio
 import logging as _logging
 from dataclasses import dataclass as _dataclass
-from typing import Any, Dict, List, Optional, Set, TypeVar
+from typing import Any, TypeVar
 
 from .. import _base_classes, _exceptions
 
@@ -27,7 +27,7 @@ class _Selected:
     receiver gets closed.
     """
 
-    inner: Optional[Any]
+    inner: Any
 
 
 @_dataclass
@@ -40,7 +40,7 @@ class _ReadyReceiver:
     When a channel has closed,  `recv` should be `None`.
     """
 
-    recv: Optional[_base_classes.Receiver[Any]]
+    recv: _base_classes.Receiver[Any] | None
 
     def get(self) -> _Selected:
         """Consume a message from the receiver and return a `_Selected` object.
@@ -100,14 +100,14 @@ def __init__(self, **kwargs: _base_classes.Receiver[Any]) -> None:
             **kwargs: sequence of receivers
         """
         self._receivers = kwargs
-        self._pending: Set[_asyncio.Task[bool]] = set()
+        self._pending: set[_asyncio.Task[bool]] = set()
 
         for name, recv in self._receivers.items():
             self._pending.add(_asyncio.create_task(recv.ready(), name=name))
 
         self._ready_count = 0
         self._prev_ready_count = 0
-        self._result: Dict[str, Optional[_ReadyReceiver]] = {
+        self._result: dict[str, _ReadyReceiver | None] = {
             name: None for name in self._receivers
         }
 
@@ -137,7 +137,7 @@ async def ready(self) -> bool:
         # pylint: disable=too-many-nested-blocks
         if self._ready_count > 0:
             if self._ready_count == self._prev_ready_count:
-                dropped_names: List[str] = []
+                dropped_names: list[str] = []
                 for name, value in self._result.items():
                     if value is not None:
                         dropped_names.append(name)
@@ -184,7 +184,7 @@ async def ready(self) -> bool:
             self._pending.add(_asyncio.create_task(recv.ready(), name=name))
         return True
 
-    def __getattr__(self, name: str) -> Optional[Any]:
+    def __getattr__(self, name: str) -> Any:
         """Return the latest unread message from a `Receiver`, if available.
 
         Args: