| Topfree is a semantic variant on the word topless. Where toplessness has already been invested with meaning of voyeurism or scandal, topfreedom presents the idea of the liberty of an individual woman or man to exist in private or public spaces without covering their nipples.
This issue is largely centred around a woman's right to bare her breasts, as this right has been conferred upon men in most cultures and contexts, anyway. To this end, many advocates of topfreedom lobby for the right to go without a top in situations where men also have this freedom.
In practice, going topfree is largely an issue of sunbathing on beaches, as is done in Europe and Australia, or of breastfeeding one's child. However, topfreedom advocates argue that this right should extend to situations of women mowing a lawn, or swimming, or playing in a park.
What the choice to go topfree is not meant to cover is entering shopping centres, restaurants, or public transit without a top, as this is not a right which has been afforded to men.
An argument often presented against women going topfree is that women are simply different; that their larger breasts, or that the increased sensitivity of their nipples, make it necessarily socially impracticable that these can be exposed. The notion of "larger" or "increased sensitivity" implies a normatively male standard for what a chest should be like. American topfree advocates may cite Amendment XIV of The Constitution of the United States of America, stating that equal protection was not applied.
Another reason argued against topfree women is that children should not be exposed to women's breasts(!) Though most infants were raised with a great deal of exposure to a woman's breasts, and though children of all ages have been exposed to men's breasts, women's breasts are still seen as indecent within the healthy development of a child. Spivak would surely have something to say on this.
Regarding children, they are commonly allowed to run around in parks, on beaches, in their yards, or at swimming pools (walk please, don't run) topfree regardless of their sex. Some public swimming pools have tried to impose upper age limits for girls going topfree (I have seen upper limits of 3, 5, 6, and 8 years). Private pools are allowed to impose what rules they will; this is rarely contested.
Another argument made by legislators is that topfreedom can be exploited for commercial purpose (as in toplessness), as promotion outside a strip club, or brothel. This is where there is some split within the arguments for what "topfree" is meant to include. Some will say that topfreedom should be limited to non-commercial purposes, and others argue in favour of the essential right of women to be bare-chested in the same capacities as men.
Groups* which advocate topfreedom:
Some* places that have legislated topfreedom for women:
People* involved in topfreedom activism:
*List is by no means exhaustive. Please contact me if you have any additions that I have not yet listed. | 
