In this note we first give a summary that on property of a remainder of a non-locally compact topological group $G$ in a compactification $bG$ makes the remainder and the topological group $G$ all separable and metrizable. If a non-locally compact topological group $G$ has a compactification $bG$ such that the remainder $bG\setminus G$ of $G$ belongs to $\mathcal {P}$, then $G$ and $bG\setminus G$ are separable and metrizable, where $\mathcal {P}$ is a class of spaces which satisfies the following conditions: (1) if $X\in \mathcal {P}$, then every compact subset of the space $X$ is a $G_\delta $-set of $X$; (2) if $X\in \mathcal {P}$ and $X$ is not locally compact, then $X$ is not locally countably compact; (3) if $X\in \mathcal {P}$ and $X$ is a Lindelöf $p$-space, then $X$ is metrizable. Some known conclusions on topological groups and their remainders can be obtained from this conclusion. As a corollary, we have that if a non-locally compact topological group $G$ has a compactification $bG$ such that compact subsets of $bG\setminus G$ are $G_{\delta }$-sets in a uniform way (i.e., $bG\setminus G$ is CSS), then $G$ and $bG\setminus G$ are separable and metrizable spaces. In the last part of this note, we prove that if a non-locally compact topological group $G$ has a compactification $bG$ such that the remainder $bG\setminus G$ has a point-countable weak base and has a dense subset $D$ such that every point of the set $D$ has countable pseudo-character in the remainder $bG\setminus G$ (or the subspace $D$ has countable $\pi $-character), then $G$ and $bG\setminus G$ are both separable and metrizable.
The concept of „tradition“ has been studied in the social sciences fo r at least two centuries and over that period every discipline has created its own variant or specialist interpretation of the term. In ethnography and ethnology research on tradition is one of the fündamental themes of scholarship, and was and is studied mainly from the perspective of external observers - i. e. members of the scholarly community. In our own researches we meet this concept only rarely and, moreover, we may find that our informants understand historicity in a way different from us; they can also think in terms of static time. This situation can be illustrated by examples from central Slovakia and Southern Moravia. It appears that we have to reckon with a double understanding and double labelling of the same phenomenon - once in historically unclarified terms (at the level of data collection) and then for a second time in historically more precise terms of „tradition“ (at the level of data processing). The historically unclarified terms are converted into more precise terms by the researcher, so that he can bring the apparently unchanging world of small communities (villages and towns) nearer to the changing world of great national and State communities. The world of the small communities then uses general terms from the outside world - among them „tradition“ - in situations of mutual contact between the two worlds. Thus „tradition“ is not merely an interesting academie problem with which the social sciences are stili wrestling in their second century of existence, but also an important transmission lever between existing microworlds and macroworlds.