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The FTSE 100 entered bull market territory yesterday as Theresa May became the only candidate remaining in the race to replace David Cameron as the UK's PM.
British stocks are 20% higher than they were when record lows were recorded in February.
Shares have been supported by speculation that the Bank of England intends to cut interest rates from 0.5% to 0.25% on Thursday.
Ireland's ISEQ closed up 109 at 5,689.
Spain and Portugal are unlikely to be fined for breaking EU deficit rules - instead they will be asked to make extra budget cuts.
"When you have rules you need to respect them. And, at the same time, we can show that those rules are intelligent, that they are not a punishment, that they are not a constraint," European Commissioner for Economics, Pierre Moscovici said.
He added that the EU did not want to impose measures which would hurt growth and job creation.
"From Ireland's point of view, it would be sufficient to have the finding that they were in breach ... We're not interested in having sanctions apply to them," Finance Minister, Michael Noonan said.
The IMF's annual report on the Italian economy says that the state is in the middle of what will be a two-decade long period of stagnation.
It believes that it will not fully shake off the effects of the 2008 crash until the mid 2020's.
The report added that the process will be "prolonged and subject to risks."
Yesterday, Eurogroup president, Jeroen Dijsselbloem has said that Italy's banking sector will be dealt with "gradually" and that its current difficulties do not amount to an "acute crisis."
Mr Dijsselbloem stressed the need for Euro states to respect the "strict" new rules which have been introduced to require creditors to take losses before public money can be put into banks.
"There have always been, and will always be, bankers who say we need more public money to recapitalise our banks, and I will resist that very strongly, because again and again it’s hitting on the taxpayer, again and again increasing sovereign debt in countries that are heavily indebted," the Dutch representative told the media.
Ten employees at the Central Bank Mint - which manufactures bank notes and coins - are to begin day two of their strike later this morning, in a dispute over pay.
The 10 maintenance technicians belong to the Unite and the Technical Engineering and Electrical Union.
They have warned that if the dispute is not resolved this week, there will be a two day stoppage from Monday 18th of July, escalating to an indefinite strike later in the month.
However, the Central Bank has stressed the industrial action will not affect the availability of notes and coins in the banking and retail sectors.