Yes, a US based fund that invests in US companies can raise from LPs in different countries, but they must follow both the regulations in the US, where the fund is domiciled, and the regulations in the country where the LP is located. The European Union, the UK, and Singapore all have complex regulations around fundraising for venture capital funds, requiring the fund manager to have licenses and meet other regulatory requirements to raise money from limited partners. It is important to know the regulatory requirements where your LPs are located by doing research and consulting with professionals.