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In semantic segmentation knowing about all existing classes is essential to yield effective results with the majority of existing approaches. However, these methods trained in a Closed Set of classes fail when new classes are found in the test phase. It means that they are not suitable for Open Set scenarios, which are very common in real-world computer vision and remote sensing applications. In this paper, we discuss the limitations of Closed Set segmentation and propose two fully convolutional approaches to effectively address Open Set semantic segmentation: OpenFCN and OpenPCS. OpenFCN is based on the well-known OpenMax algorithm, configuring a new application of this approach in segmentation settings. OpenPCS is a fully novel approach based on feature-space from DNN activations that serve as features for computing PCA and multi-variate gaussian likelihood in a lower dimensional space. Experiments were conducted on the well-known Vaihingen and Potsdam segmentation datasets. OpenFCN showed little-to-no improvement when compared to the simpler and much more time efficient SoftMax thresholding, while being between some orders of magnitude slower. OpenPCS achieved promising results in almost all experiments by overcoming both OpenFCN and SoftMax thresholding. OpenPCS is also a reasonable compromise between the runtime performances of the extremely fast SoftMax thresholding and the extremely slow OpenFCN, being close able to run close to real-time. Experiments also indicate that OpenPCS is effective, robust and suitable for Open Set segmentation, being able to improve the recognition of unknown class pixels without reducing the accuracy on the known class pixels.