diff --git a/intervals/__init__.py b/intervals/__init__.py
index 5241270..4c949ad 100644
--- a/intervals/__init__.py
+++ b/intervals/__init__.py
@@ -50,6 +50,9 @@ def canonicalize(interval, lower_inc=True, upper_inc=False):
     if not interval.discrete:
         raise TypeError('Only discrete ranges can be canonicalized')
 
+    if interval.empty:
+        return interval
+
     lower, lower_inc = canonicalize_lower(interval, lower_inc)
     upper, upper_inc = canonicalize_upper(interval, upper_inc)
 
@@ -69,6 +72,21 @@ def wrapper(self, arg):
     return wrapper
 
 
+class ClosedInterval(type):
+    """
+    Supports initialization of intervals using square brackets and makes them
+    closed intervals.
+
+    eg.
+
+    IntInterval[1, 4] == IntInterval([1, 4])
+    """
+    def __getitem__(self, bounds):
+        lower_inc = upper_inc = True
+        return self(bounds, lower_inc, upper_inc)
+
+
+@six.add_metaclass(ClosedInterval)
 @total_ordering
 class AbstractInterval(object):
     step = None
@@ -148,6 +166,20 @@ def __init__(
             30
 
         """
+
+        # This if-block adds support for parentheses as open intervals.
+        # Note: If the interval is initialized with the parentheses with two
+        #       objects of same type, eg.
+        #       IntInterval(1, 4)
+        #       the bounds and lower_inc are received of that type and
+        #       upper_inc is None.
+        #
+        # eg.
+        # IntInterval(1, 4) == IntInterval((1, 4))
+        if type(bounds) == type(lower_inc) and not upper_inc:
+            bounds = (bounds, lower_inc)
+            lower_inc = upper_inc = None
+
         self.lower, self.upper, self.lower_inc, self.upper_inc = (
             self.parser(bounds, lower_inc, upper_inc)
         )
@@ -307,6 +339,18 @@ def radius(self):
     def degenerate(self):
         return self.upper == self.lower
 
+    @property
+    def empty(self):
+        if self.discrete and not self.degenerate:
+            return (
+                self.upper - self.lower == self.step
+                and not (self.upper_inc or self.lower_inc)
+            )
+        return (
+            self.upper == self.lower
+            and not (self.lower_inc and self.upper_inc)
+        )
+
     @property
     def centre(self):
         return float((self.lower + self.upper)) / 2
@@ -365,16 +409,27 @@ def __and__(self, other):
         """
         Defines the intersection operator
         """
+        if self.upper < other.lower or other.upper < self.lower:
+            return self.__class__((0, 0))
         if self.lower <= other.lower <= self.upper:
-            return self.__class__([
+            intersection = self.__class__([
                 other.lower,
                 other.upper if other.upper < self.upper else self.upper
             ])
+            intersection.lower_inc = other.lower_inc
+            intersection.upper_inc = (
+                other.upper_inc if other.upper < self.upper else self.upper_inc
+            )
         elif self.lower <= other.upper <= self.upper:
-            return self.__class__([
+            intersection = self.__class__([
                 other.lower if other.lower > self.lower else self.lower,
                 other.upper
             ])
+            intersection.lower_inc = (
+                other.lower_inc if other.lower > self.lower else self.lower_inc
+            )
+            intersection.upper_inc = other.upper_inc
+        return intersection
 
 
 class IntInterval(AbstractInterval):
diff --git a/tests/test_initialization.py b/tests/test_initialization.py
index 6840bb8..eaac817 100644
--- a/tests/test_initialization.py
+++ b/tests/test_initialization.py
@@ -88,6 +88,12 @@ def test_supports_integers(self):
         assert interval.lower_inc
         assert interval.upper_inc
 
+    def test_uses_two_numbers_with_parentheses_as_open_interval(self):
+        assert IntInterval(1, 2) == IntInterval((1, 2))
+
+    def test_uses_two_numbers_with_square_brackets_as_closed_interval(self):
+        assert IntInterval[1, 2] == IntInterval([1, 2])
+
     @mark.parametrize('number_range',
         (
             (3, 2),
diff --git a/tests/test_operators.py b/tests/test_operators.py
index 731dee7..161c9ee 100644
--- a/tests/test_operators.py
+++ b/tests/test_operators.py
@@ -63,3 +63,28 @@ class TestDiscreteRangeComparison(object):
     ))
     def test_eq_operator(self, interval, interval2):
         assert IntInterval(interval) == IntInterval(interval2)
+
+
+class TestBinaryOperators(object):
+    @mark.parametrize(('interval1', 'interval2', 'result'), (
+        ((2, 3), (3, 4), (3, 3)),
+        ((2, 3), [3, 4], '[3, 3)'),
+        ((2, 5), (3, 10), (3, 5)),
+        ('(2, 3]', '[3, 4)', [3, 3]),
+        ('(2, 10]', '[3, 40]', [3, 10]),
+        ((2, 10), (3, 8), (3, 8)),
+    ))
+    def test_and_operator(self, interval1, interval2, result):
+        assert (
+            IntInterval(interval1) & IntInterval(interval2) ==
+            IntInterval(result)
+        )
+
+    @mark.parametrize(('interval1', 'interval2', 'empty'), (
+        ((2, 3), (3, 4), True),
+        ((2, 3), [3, 4], True),
+        ([2, 3], (3, 4), True),
+        ('(2, 3]', '[3, 4)', False),
+    ))
+    def test_and_operator_for_empty_results(self, interval1, interval2, empty):
+        assert (IntInterval(interval1) & IntInterval(interval2)).empty == empty
diff --git a/tests/test_properties.py b/tests/test_properties.py
index cf8c4a5..a818586 100644
--- a/tests/test_properties.py
+++ b/tests/test_properties.py
@@ -70,6 +70,21 @@ def test_open(self, number_range, is_open):
     def test_closed(self, number_range, is_closed):
         assert IntInterval(number_range).closed == is_closed
 
+    @mark.parametrize(('number_range', 'empty'),
+        (
+            ((2, 3), True),
+            ([2, 3], False),
+            ([2, 2], False),
+            ((2, 2), True),
+            ('[2, 2)', True),
+            ('(2, 2]', True),
+            ('[2, 3)', False),
+            ((2, 10), False),
+        )
+    )
+    def test_empty(self, number_range, empty):
+        assert IntInterval(number_range).empty == empty
+
     @mark.parametrize(('number_range', 'degenerate'),
         (
             ((2, 4), False),