The Internet of Things (IoT) today is a large set of technologies and platforms for sensor and actuation applications in smart-health, transportation, metering, city and building management, etc. Most of these IoT platforms are designed as isolated systems and are distributed across the composite space of devices, interconnected with complex control layers, often distributed as cloud services. The H2020 symbIoTe R&D project originated from the need to design new solutions and approaches to achieve symbiosis of smart objects across different IoT environments. In symbIoTe we have developed novel methodologies to enable federations of vertical IoT silos and allow various levels of interoperation among IoT platforms, devices and applications. This paper describes the architecture of the symbIoTe Smart Space (SSP), a concept which has been developed by the authors to cover functions, interfaces, and resources that allow one or more IoT platforms to provide coordinated services to their users. The SSP architecture supports discovery for various types of sensors and actuators, coordinates access to the resources (i.e. the symbIoTe Devices) and implements security services establishing trust relationship for the actions on IoT resources. The SSP solution developed in symbIoTe is being evaluated in some reference use cases of the project, two of which of particular interest for the authors: namely, a Smart Residence use case designed to validate the interoperability across different smart home IoT solutions, and a Smart Yachting use case designed to implement the interoperation between the IoT platforms on yachts and the ones available in marinas.