A) Monomer units derived from monomers containing free, partially or fully salified strong acid functional groups in a molar ratio of 50% or more and 99% or less, with respect to 100 mol%, b) 1% or more and 50% The following molar ratio of formula (I): CH2 = CH (R1) -C (= O) -O- (CH2) n-CF3 (I) (in formula (I), radical R1 represents a hydrogen atom or a methyl radical. N represents an integer equal to 1, 2 or 3), c) optionally at least one formula (II): R2-C (= O)-in a molar ratio of more than 0% and not more than 5 mol% O — [(CH 2 —CH (R 4) —O] m —R 3 (II) (wherein m represents a number of 0 to 50 and R 2 contains 2 to 4 carbon atoms) Represents an unsaturated aliphatic monovalent radical, R4 represents a hydrogen atom, a methyl radical or an ethyl radical； R3 represents a linear or branched, saturated or unsaturated aliphatic hydrocarbon radical containing 8 to 30 carbon atoms) and monomer units derived from d) optionally 0% A linear, branched or cross-linked anionic polyelectrolyte obtained by polymerization of at least one monomer having a diethylene or polyethylene cross-linkage in a molar ratio of more than 5%. Its use as a thickener for topical compositions. [Selection figure] None１００ｍｏｌ％に対して、ａ）５０％以上かつ９９％以下のモル比の遊離の、部分的に又は完全に塩化した強酸官能基を含むモノマーに由来するモノマー単位、ｂ）１％以上かつ５０％以下のモル比の式（Ｉ）：ＣＨ２＝ＣＨ（Ｒ１）－Ｃ（＝Ｏ）－Ｏ－（ＣＨ２）ｎ－ＣＦ３（Ｉ）（式（Ｉ）中、ラジカルＲ１は水素原子又はメチルラジカルを表し、ｎは１、２又は３に等しい整数を表す）のモノマー、ｃ）任意で、０％超かつ５ｍｏｌ％以下のモル比の少なくとも１つの式（ＩＩ）：Ｒ２－Ｃ（＝Ｏ）－Ｏ－［（ＣＨ２－ＣＨ（Ｒ４）－Ｏ］ｍ－Ｒ３（ＩＩ）（式（ＩＩ）中、ｍは０以上かつ５０以下の数を表し、Ｒ２は２個～４個の炭素原子を含む不飽和の脂肪族一価ラジカルを表し、Ｒ４は水素原子、メチルラジカル又はエチルラジカルを表し、Ｒ３は８個～３０個の炭素原子を含む線状又は分岐、飽和又は不飽和の脂肪族炭化水素ラジカルを表す）のモノマーに由来するモノマー単位、及びｄ）任意で、０％超かつ５％以下のモル比のジエチレン系又はポリエチレン系架橋を有する少なくとも１つのモノマーの重合によって得られる線状、分岐又は架橋アニオン性高分子電解質。局所組成物の増粘剤としてのその使用。【選択図】なし
