diff --git a/packages/tpetra/core/compat/Tpetra_KokkosCompat_ClassicNodeAPI_Wrapper.hpp b/packages/tpetra/core/compat/Tpetra_KokkosCompat_ClassicNodeAPI_Wrapper.hpp
index d8d146bb3348..19c6aa492ce0 100644
--- a/packages/tpetra/core/compat/Tpetra_KokkosCompat_ClassicNodeAPI_Wrapper.hpp
+++ b/packages/tpetra/core/compat/Tpetra_KokkosCompat_ClassicNodeAPI_Wrapper.hpp
@@ -43,6 +43,18 @@ class KokkosDeviceWrapperNode {
   /// release.  This Node type is safe to use.
   static constexpr bool classic = false;
 
+  //! Whether the ExecutionSpace is Kokkos::Serial.
+#ifdef KOKKOS_ENABLE_SERIAL
+  static constexpr bool is_serial = std::is_same_v<ExecutionSpace, Kokkos::Serial>;
+#else
+  static constexpr bool is_serial = false;
+#endif
+
+  //! Whether the ExecutionSpace is CPU-like (its default memory space is HostSpace)
+  static constexpr bool is_cpu = std::is_same_v<typename ExecutionSpace::memory_space, Kokkos::HostSpace>;
+  //! Whether the ExecutionSpace is GPU-like (its default memory space is not HostSpace)
+  static constexpr bool is_gpu = !is_cpu;
+
   KokkosDeviceWrapperNode (Teuchos::ParameterList& /* params */) = delete;
   KokkosDeviceWrapperNode () = delete;