  The cross-blockchain transaction remains one of the most challenging problems
in blockchains. The root cause of the challenge lies in the nondeterministic
nature of blockchains: A $n$-party transaction across multiple blockchains
might be partially rolled back due to the potential forks in any of the
participating blockchains---eventually, only one fork will survive in the
competition among miners. While some effort has recently been made to
developing hierarchically distributed commit protocols to make multi-party
transactions progress, there is no systematic method to reason about the
transaction outcome. This paper tackles this problem from a perspective of
point-set topology. We construct multiple topological spaces for the
transactions and blockchain forks, and show that these spaces are internally
related through either homeomorphism or continuous functions. Combined
together, these tools allow us to reason about the cross-blockchain
transactions through the growing-fork topology, an intuitive representation of
blockchains.
