diff --git a/navix/__init__.py b/navix/__init__.py
index 0aa49da..d809db3 100644
--- a/navix/__init__.py
+++ b/navix/__init__.py
@@ -29,4 +29,5 @@
     environments,
     terminations,
     config,
+    spaces,
 )
diff --git a/navix/_version.py b/navix/_version.py
index 011f80c..a4beb31 100644
--- a/navix/_version.py
+++ b/navix/_version.py
@@ -18,5 +18,5 @@
 # under the License.
 
 
-__version__ = "0.3.7"
+__version__ = "0.3.8"
 __version_info__ = tuple(int(i) for i in __version__.split(".") if i.isdigit())
diff --git a/navix/entities.py b/navix/entities.py
index 0b7b332..c667f49 100644
--- a/navix/entities.py
+++ b/navix/entities.py
@@ -241,7 +241,9 @@ def transparent(self) -> Array:
 
     @property
     def sprite(self) -> Array:
-        sprite = SPRITES_REGISTRY[Entities.DOOR.value][self.direction, jnp.asarray(self.open, dtype=jnp.int32)]
+        sprite = SPRITES_REGISTRY[Entities.DOOR.value][
+            self.direction, jnp.asarray(self.open, dtype=jnp.int32)
+        ]
         if sprite.ndim == 3:
             # batch it
             sprite = sprite[None]
diff --git a/navix/environments/environment.py b/navix/environments/environment.py
index 0b2781b..225965d 100644
--- a/navix/environments/environment.py
+++ b/navix/environments/environment.py
@@ -20,6 +20,7 @@
 
 from __future__ import annotations
 
+import sys
 import abc
 from enum import IntEnum
 from typing import Any, Callable, Dict
@@ -31,9 +32,10 @@
 
 
 from .. import tasks, terminations, observations
-from ..graphics import RenderingCache
+from ..graphics import RenderingCache, TILE_SIZE
 from ..entities import State
 from ..actions import ACTIONS
+from ..spaces import Space, Discrete, Continuous
 
 
 class StepType(IntEnum):
@@ -77,6 +79,39 @@ class Environment(struct.PyTreeNode):
         pytree_node=False, default=terminations.on_navigation_completion
     )
 
+    @property
+    def observation_space(self) -> Space:
+        if self.observation_fn == observations.none:
+            return Continuous(shape=())
+        elif self.observation_fn == observations.categorical:
+            return Discrete(sys.maxsize, shape=(self.height, self.width))
+        elif self.observation_fn == observations.categorical_first_person:
+            radius = observations.RADIUS
+            return Discrete(sys.maxsize, shape=(radius + 1, radius * 2 + 1))
+        elif self.observation_fn == observations.rgb:
+            return Discrete(
+                256,
+                shape=(self.height * TILE_SIZE, self.width * TILE_SIZE, 3),
+                dtype=jnp.uint8,
+            )
+        elif self.observation_fn == observations.rgb_first_person:
+            radius = observations.RADIUS
+            return Discrete(
+                256,
+                shape=(radius * TILE_SIZE * 2 + 1, radius * TILE_SIZE * 2 + 1, 3),
+                dtype=jnp.uint8,
+            )
+        else:
+            raise NotImplementedError(
+                "Unknown observation space for observation function {}".format(
+                    self.observation_fn
+                )
+            )
+
+    @property
+    def action_space(self) -> Space:
+        return Discrete(len(ACTIONS))
+
     @abc.abstractmethod
     def reset(self, key: KeyArray, cache: RenderingCache | None = None) -> Timestep:
         raise NotImplementedError()
diff --git a/navix/environments/keydoor.py b/navix/environments/keydoor.py
index 6f8c8b0..cb3e628 100644
--- a/navix/environments/keydoor.py
+++ b/navix/environments/keydoor.py
@@ -14,8 +14,12 @@
 class KeyDoor(Environment):
     def reset(self, key: KeyArray, cache: Union[RenderingCache, None] = None) -> Timestep:  # type: ignore
         # check minimum height and width
-        assert self.height > 3, f"Room height must be greater than 3, got {self.height} instead"
-        assert self.width > 4, f"Room width must be greater than 5, got {self.width} instead"
+        assert (
+            self.height > 3
+        ), f"Room height must be greater than 3, got {self.height} instead"
+        assert (
+            self.width > 4
+        ), f"Room width must be greater than 5, got {self.width} instead"
 
         key, k1, k2, k3, k4 = jax.random.split(key, 5)
 
@@ -39,13 +43,19 @@ def reset(self, key: KeyArray, cache: Union[RenderingCache, None] = None) -> Tim
         wall_cols = jnp.asarray([door_col] * (self.height - 2))
         wall_pos = jnp.stack((wall_rows, wall_cols), axis=1)
         # remove wall where the door is
-        wall_pos = jnp.delete(wall_pos, door_row - 1, axis=0, assume_unique_indices=True)
+        wall_pos = jnp.delete(
+            wall_pos, door_row - 1, axis=0, assume_unique_indices=True
+        )
         walls = Wall(position=wall_pos)
 
         # get rooms
-        first_room_mask = mask_by_coordinates(grid, (jnp.asarray(self.height), door_col), jnp.less)
+        first_room_mask = mask_by_coordinates(
+            grid, (jnp.asarray(self.height), door_col), jnp.less
+        )
         first_room = jnp.where(first_room_mask, grid, -1)  # put walls where not mask
-        second_room_mask = mask_by_coordinates(grid, (jnp.asarray(0), door_col), jnp.greater)
+        second_room_mask = mask_by_coordinates(
+            grid, (jnp.asarray(0), door_col), jnp.greater
+        )
         second_room = jnp.where(second_room_mask, grid, -1)  # put walls where not mask
 
         # spawn player
diff --git a/navix/environments/room.py b/navix/environments/room.py
index 4e6804f..de6918f 100644
--- a/navix/environments/room.py
+++ b/navix/environments/room.py
@@ -19,13 +19,12 @@
 
 
 from __future__ import annotations
-from typing import Callable, Union
+from typing import Union
 
 import jax
 import jax.numpy as jnp
 from jax.random import KeyArray
 
-
 from ..components import EMPTY_POCKET_ID
 from ..entities import Entities, Goal, Player, State
 from ..grid import random_positions, random_directions, room
diff --git a/navix/grid.py b/navix/grid.py
index 09c912c..eb8440e 100644
--- a/navix/grid.py
+++ b/navix/grid.py
@@ -181,7 +181,7 @@ def crop(grid: Array, origin: Array, direction: Array, radius: int) -> Array:
         cropped,
     )
 
-    cropped = rotated[:radius + 1]
+    cropped = rotated[: radius + 1]
     return jnp.asarray(cropped, dtype=grid.dtype)
 
 
diff --git a/navix/observations.py b/navix/observations.py
index 99221e5..2ff6d0e 100644
--- a/navix/observations.py
+++ b/navix/observations.py
@@ -30,6 +30,9 @@
 from .grid import align, idx_from_coordinates, crop, view_cone
 
 
+RADIUS = 3
+
+
 def none(
     state: State,
 ) -> Array:
@@ -52,7 +55,6 @@ def categorical(
 
 def categorical_first_person(
     state: State,
-    radius: int = 3,
 ) -> Array:
     # get transparency map
     transparency_map = jnp.where(state.grid == 0, 1, 0)
@@ -62,14 +64,14 @@ def categorical_first_person(
 
     # apply view mask
     player = state.get_player()
-    view = view_cone(transparency_map, player.position, radius)
+    view = view_cone(transparency_map, player.position, RADIUS)
 
     # get categorical representation
     tags = state.get_tags()
     obs = state.grid.at[tuple(positions.T)].set(tags) * view
 
     # crop grid to agent's view
-    obs = crop(obs, player.position, player.direction, radius)
+    obs = crop(obs, player.position, player.direction, RADIUS)
 
     return obs
 
@@ -99,7 +101,6 @@ def rgb(
 
 def rgb_first_person(
     state: State,
-    radius: int = 3,
 ) -> Array:
     # calculate final image size
     image_size = (
@@ -113,7 +114,7 @@ def rgb_first_person(
     transparent = state.get_transparency()
     transparency_map = transparency_map.at[tuple(positions.T)].set(~transparent)
     player = state.get_player()
-    view = view_cone(transparency_map, player.position, radius)
+    view = view_cone(transparency_map, player.position, RADIUS)
     view = jax.image.resize(view, image_size, method="nearest")
     view = jnp.tile(view[..., None], (1, 1, 3))
 
@@ -131,7 +132,7 @@ def rgb_first_person(
     patchwork = patches.reshape(*state.grid.shape, *patches.shape[1:])
 
     # crop grid to agent's view
-    patchwork = crop(patchwork, player.position, player.direction, radius)
+    patchwork = crop(patchwork, player.position, player.direction, RADIUS)
 
     # reconstruct image
     obs = jnp.swapaxes(patchwork, 1, 2)
diff --git a/navix/spaces.py b/navix/spaces.py
new file mode 100644
index 0000000..66e0011
--- /dev/null
+++ b/navix/spaces.py
@@ -0,0 +1,70 @@
+# Copyright [2023] The Helx Authors.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+
+from __future__ import annotations
+from typing import Callable
+
+import jax
+import jax.numpy as jnp
+from jax.random import KeyArray
+
+from jax.core import Shape
+from jax import Array
+from jax.core import ShapedArray, Shape
+
+
+POS_INF = jnp.asarray(1e16)
+NEG_INF = jnp.asarray(-1e16)
+
+
+class Space(ShapedArray):
+    minimum: Array = NEG_INF
+    maximum: Array = POS_INF
+
+    def __repr__(self):
+        return "{}, min={}, max={})".format(
+            super().__repr__()[:-1], self.minimum, self.maximum
+        )
+
+    def sample(self, key: KeyArray) -> Array:
+        raise NotImplementedError()
+
+
+class Discrete(Space):
+    def __init__(self, n_elements: int, shape: Shape = (), dtype=jnp.int32):
+        super().__init__(shape, dtype)
+        self.minimum = jnp.asarray(0)
+        self.maximum = jnp.asarray(n_elements - 1)
+
+    def sample(self, key: KeyArray) -> Array:
+        return jax.random.randint(
+            key, self.shape, self.minimum, self.maximum, self.dtype
+        )
+
+
+class Continuous(Space):
+    def __init__(self, shape: Shape = (), minimum=NEG_INF, maximum=POS_INF):
+        super().__init__(shape, jnp.float32)
+        self.minimum = minimum
+        self.maximum = maximum
+
+    def sample(self, key: KeyArray) -> Array:
+        assert jnp.issubdtype(self.dtype, jnp.floating)
+        # see: https://github.com/google/jax/issues/14003
+        lower = jnp.nan_to_num(self.minimum)
+        upper = upper = jnp.nan_to_num(self.maximum)
+        return jax.random.uniform(
+            key, self.shape, minval=lower, maxval=upper, dtype=self.dtype
+        )
diff --git a/tests/test_environments.py b/tests/test_environments.py
index 3d2c06c..48d6bf6 100644
--- a/tests/test_environments.py
+++ b/tests/test_environments.py
@@ -83,4 +83,4 @@ def test_keydoor2():
     # test_room()
     # jax.jit(test_room)()
     # test_keydoor()
-    test_keydoor2()
\ No newline at end of file
+    test_keydoor2()