Aoa, I was wondering that if a women does not take hijab but dresses very modestly and keeps her hair tied up and is very religious in other aspects,does that make her of those in the hadees mentioned of sinning openly,a mujahirin?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

First of all, you should know that it is not a condition for the Hijab to have a certain color or to be a specific type of dress; any dress that meets the conditions of an Islamic dress is considered Hijab. Hence you will know whether or not it is possible for what you described as being modest to be a Hijab. Please refer to Fatwa 84066.

Also, it should be noted that the Hijab is an obligation for a Muslim woman; it is not permissible for her to be negligent about it, or else she will be sinful. For the evidence that the Hijab is an Islamic obligation, please refer to Fatwa 84053.

The open sinners (Mujaahireen) are those who commit sins in public and are known for doing so, as defined by the scholars. A woman who does not abide by the Hijab and goes out while revealing her ‘Awrah (parts of the body that must be covered in Islam) is included among those who sin openly. The more temptation her dress causes, the more sinful she is. Shaykh Al-Islam Ibn Taymiyyah said in his commentary on the Hadeeth: "All my Ummah is pardoned except the open sinners": "As long as the sin is concealed, the sin is peculiar to its doer, but if the doer displays his sin and he does not reject it, then its harm extends to others, especially if he incites others to do it when displaying it. It is for this reason that Imaam Ahmad rejected romantic poetry, for fear that the souls would be incited to commit immoralities." [End of quote]

There is no doubt that not wearing the Hijab is among the things that causes immorality.

Allaah Knows best.