how can we impliment offline payment without the blockchain, at least we can check if the coin is valid if the blockchain on the sellers computer is recent we can ensure no double spending until the last time the blockchain was Synced.
I think, when you talk about "blockchain", you actually mean the "UTXO set" or even "account balances". When you trust the central server, you can simply keep a list of balances at each address (or the UTXO set) to validate coins. Still no need to do a blockchain with mining and all that.
BTW, you could look into Chaumian cash.