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diff --git a/src/main/java/org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.java b/src/main/java/org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.java
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+++ b/src/main/java/org/apache/commons/math3/geometry/euclidean/oned/Euclidean1D.java
@@ -0,0 +1,100 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You 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.
+ */
+
+package org.apache.commons.math3.geometry.euclidean.oned;
+
+import java.io.Serializable;
+
+import org.apache.commons.math3.exception.MathUnsupportedOperationException;
+import org.apache.commons.math3.exception.util.LocalizedFormats;
+import org.apache.commons.math3.geometry.Space;
+
+/**
+ * This class implements a one-dimensional space.
+ * @since 3.0
+ */
+public class Euclidean1D implements Serializable, Space {
+
+    /** Serializable version identifier. */
+    private static final long serialVersionUID = -1178039568877797126L;
+
+    /** Private constructor for the singleton.
+     */
+    private Euclidean1D() {
+    }
+
+    /** Get the unique instance.
+     * @return the unique instance
+     */
+    public static Euclidean1D getInstance() {
+        return LazyHolder.INSTANCE;
+    }
+
+    /** {@inheritDoc} */
+    public int getDimension() {
+        return 1;
+    }
+
+    /** {@inheritDoc}
+     * <p>
+     * As the 1-dimension Euclidean space does not have proper sub-spaces,
+     * this method always throws a {@link NoSubSpaceException}
+     * </p>
+     * @return nothing
+     * @throws NoSubSpaceException in all cases
+     */
+    public Space getSubSpace() throws NoSubSpaceException {
+        throw new NoSubSpaceException();
+    }
+
+    // CHECKSTYLE: stop HideUtilityClassConstructor
+    /** Holder for the instance.
+     * <p>We use here the Initialization On Demand Holder Idiom.</p>
+     */
+    private static class LazyHolder {
+        /** Cached field instance. */
+        private static final Euclidean1D INSTANCE = new Euclidean1D();
+    }
+    // CHECKSTYLE: resume HideUtilityClassConstructor
+
+    /** Handle deserialization of the singleton.
+     * @return the singleton instance
+     */
+    private Object readResolve() {
+        // return the singleton instance
+        return LazyHolder.INSTANCE;
+    }
+
+    /** Specialized exception for inexistent sub-space.
+     * <p>
+     * This exception is thrown when attempting to get the sub-space of a one-dimensional space
+     * </p>
+     */
+    public static class NoSubSpaceException extends MathUnsupportedOperationException {
+
+        /** Serializable UID. */
+        private static final long serialVersionUID = 20140225L;
+
+        /** Simple constructor.
+         */
+        public NoSubSpaceException() {
+            super(LocalizedFormats.NOT_SUPPORTED_IN_DIMENSION_N, 1);
+        }
+
+    }
+
+}