Geodesic
There is no universal separable Fréchet or sequential compact space
Commentationes Mathematicae Universitatis Carolinae, Tome 22 (1981) no. 1, pp. 161-168

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Classification : 54A25, 54C05, 54D55, 54D99 
Bashkirov, Aleksandr I. There is no universal separable Fréchet or sequential compact space. Commentationes Mathematicae Universitatis Carolinae, Tome 22 (1981) no. 1, pp. 161-168. http://geodesic.mathdoc.fr/item/CMUC_1981_22_1_a12/
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[11 A. I. BASHKIROV: On continuous maps of Isbell spaces and strong $0$-dimensionality. Bull. Pol. Acad. Sci. 27, 7 (1979), 605-611. | MR

[2] A. I. BASHKIROV: On Fréchet compactifications of discrete spaces. ibid. (to appear). | MR | Zbl

[3] R. ENGEIKING: General Topology. Warszawa, 1977.

[4] S. P. FRANKLIN: Spaces in which sequences suffice, II. Fund. Math. 61 (1967), 51-56. | MR | Zbl

[5] S. MRÓWKA: On completely regular spaces. ibid. 41 (1954), 105-106. | MR